What is the cutoff between the word banned and suspended?
suspension
noun
3. temporary abrogation or withholding, as of a law, privilege, decision, belief, etc.
banned
verb (used with object), banned, banning. 1. to prohibit, forbid, or bar; interdict:
Basically, a suspension is temporary and to be banned is usually taken as being permanent. So, "temporarily banned", is another way of saying suspended.
No, the whole idea behind the word "Banned" is NOT permanent nor at least quasi-permanent.
This BBC News article uses the verb "banned" as an opposite to "allowed" to list a different category which is allowed and "banned".
While ordinary tourism is still banned, the new regulations will allow US citizens to travel to Cuba for any of a dozen specific reasons without first obtaining a special licence from the government.
"Ordinary toursim" which has been banned for around 55 years could be lifted anytime when Congress decides to do so. There is no connotation of being "permanent" or "quasi-permanent" as you can read 55-year-old ban was partially lifted by the US President.
The verb "ban" means :
Officially or legally prohibit (something): ‘parking is banned around the harbour in summer’
[Oxford Online Dictionary]
The above is the first usage example in the dictionary. "Banned" is used for the prohibition of parking to be implemented "only temporarily" in Summer.
You can ban/allow something temporarily and reverse it no matter how long you ban/allow it. There is no cutoff between "banned" and "suspended" and it is subjective and arbitrary. "Banned" is stronger in meaning than "suspended" and "suspended" has a stronger connotation of possibility that something "not allowed" would be lifted sooner than "banned".
When did 'temporarily banned' begin to be used in written English?
The notion that something might be "temporarily banned" seems not to have occurred to any published writer until the 1900s. A Google Search for the terms "temporarily ban" (blue line), "temporarily banned" (red line), and "temporarily banning" (green line) yields the following Ngram chart for the years 1800–2005:
The earliest match for the any of the three phrases is from "Letter of Instructions embodying the Reforms decided upon, drawn up by the Commission appointed for the Purpose of Inquiring into the Working of the Custom-house Porters of Constantinople," in Parliamentary Papers, House of Commons (1907):
Such [disputants] as are recalcitrant, or as are shown to the Administration to have misbehaved themselves, as well as "kol-bashis" or "keïssé-dars" or porters who shall insult or behave with violence or insolence towards merchants or persons having business at the custom-house, shall be temporarily banned by the guild for periods proportionate to the degree of their offence and, in case of repetition shall be reported by the Director-General to the deputation for expulsion from the custom-house.
Here "temporarily banned" means something like "expelled with possibility of future reinstatement," or more simply "banished for a fixed term."
The next-earliest Google Books match is from Bradstreet's Weekly: A Business Digest (June 21, 1913):
Notwithstanding the disposition of leading American banking concerns to follow the example given by similar interests in London, where the underwriting and presentation of new bond issues for subscription has been temporarily banned, high rate, short-term note issues are still being brought out with a certain amount of confidence in the public's ability and readiness to absorb such investments.
Here we might have expected to see "temporarily prohibited" in place of "temporarily banned."
But though "temporarily banned" may go no farther back than 1907, "temporarily banished" yields matches from more than a century earlier. Here is the Ngram chart for "temporarily banish" (blue line), "temporarily banished" (red line), and "temporarily banishing" (green line) for the years 1800–2005:
In this case the earliest match is from Helen Williams, Sketches of the State of Manners and Opinions in the French Republic, volume 1 (1801):
And when was this boasted clemency exercised towards others, who were momentarily detained, or temporarily banished? M. Mallet has omitted to mark the precise date, but we can find evidence of the epocha in an edict, the authority of which he will not dispute, published by the government of Berne, the 15th of June, 1797, in which, on the supplication of Bonaparte, the Senate not only rehabilitated the memory of General Laharpe, condemned to the scaffold, and returned his confiscated property, but granted "an amnesty and general pardon to all who, implicated in the procedures of 1791 and 1792, were punished, or had become fugitives from their country."
And the next-earliest match is from an 1802 translation of Jean Louis Giraud Soulavie, Historical and Political Memoirs of the Reign of Lewis XVI (1802):
"... The Genevese insurgents are, on the contrary, governed and mis-led by a few wretches in the pay of Great-Britain, who have instilled into them the strange idea of blowing up Geneva, if they could not govern it. When the marquis of Jaucourt has wholly or temporarily banished them, they will retire to London; but I shall have preserved Geneva: it will not be destroyed by gunpowder: this I have promised the king."
It seems to me that neither the idea of temporarily banning people or things, nor the idea of temporarily banishing them is incoherent or self-contradictory. Nevertheless, "temporarily banish/banished/banishing" yields no Google Books matches from before 1801, and "temporarily ban/banned/banning" yields no such matches from before 1907. Before those dates, for whatever reason, English speakers and writers appear to have used other wordings to convey the sense "to prohibit or to expel without right of return for a specified or indefinite period of time, but not permanently."
Banning for a fixed amount of time
In a comment appended to this answer, RyeɃreḁd has suggested that "temporarily banned" may be acceptable only if it refers to a suspension of indefinite duration. To test this proposition, I ran searches for "banned for a year" and "banned for one year"—expressions that impose what amounts to a suspension of a specific length. The earliest instance of "banned for a year" that I've been able to find is from The Waterways Journal (1943), where it appears as a subhead:
Banned For a Year
It was believed that if a time limit is placed on the forms anyone violating the law would be banned from the rivers for a year.
And the earliest match for "banned for one year" is from The Literary Digest (1937) [combined snippets]:
To entrench his dictatorship, Colonel Franco banned, for one year, all activities by political groups "not emanating from the Revolution" he headed. He suffered only the National Independent Party, which had backed him, and the National Revolutionary Party, which he formed formed after its Mexican prototype, to exist.
This instance of "banned for one year" in connection with a dictate of Francisco Franco is replicated in The World Almanac & Book of Facts (1937), though with different surrounding wording. As events unfolded, an attempted revolt within the year of the original ban "gave President Franco a much-needed excuse to continue indefinitely the ban against the opposition parties"—but this wording reinforces the notion that a ban may be temporary (in this case, for a specified period) or indefinite (with no fixed or promised rescission).
An instance of "banned for the year," however, appears in a story about signing up for the Westminster Kennel Club dog show, "Many Special Prizes Offered for Dog Show", in the New York Tribune (January 27, 1918):
All entries close to-morrow, but those bearing that postmark will be received for a reasonable period. Under no conditions, however, will an entry be accepted after tp-morrow, and when the clock reveals midnight has been passed by even a second all new entries are banned for the year.
This last example may be seen as a poor wording of the idea "all new entries for the year are banned," but the later examples of "banned for one year" and "banned for a year" cited above clearly use banned in the sense of "prohibited" and specify a precise duration, meaning that in both instances banned could equivalently be expressed as suspended.