How can I deliver the meaning of "within a specified range"?

If I absolutely had to choose between these two alternatives, I would pick "limited between", but generally speaking, I would go with "limited to", as in:

The number of weeks for data retrieval is limited to 25–52.

(Notes: that's an en dash, I've added a the, and I don't repeat the word weeks.)

The British National Corpus does not have a single cite for "limited between" or "limited within", but it has 1343 cites for "limited to", including several cites for value ranges, e.g.:

• [...] limited to 1 to 1.5p on a pint of beer [...]
• [...] limited to 15 to 18 per cent for a transitional period [...]

It even has two cites for "limited to between" (but again, none for just "limited between").

I'd re-write it like this:

Number of weeks for data retrieval must be between 25 and 52.

Would a simple:

number of weeks (range: 25 to 52)

be enough?

What's your audience?

I ask because mathematicians, engineers and scientists have a precise way of communicating non-inclusive ranges:

• x is in (25, 52)

• 25 < x < 52

If you have a sufficiently technical audience, they'll know what that means.

Both "limited within" and "limited between" sound to me like in a certain time interval, data retrieval is limited (so if it's now 53 weeks since [something], retrieval is unlimited, while last week, it was limited). Naturally, this makes no sense in context, so there's definitely a problem somewhere.

The best solution is probably something like what VonC suggested: label the field with text that identifies the nature of the value to be entered, and then separately provide a range of valid values.