Adverb placement: "There is still" vs. "there still is"

Solution 1:

There are many different kinds of adverbs, and each one has different rules for placement.
This is one reason why knowing that some word "is an adverb" is pretty useless information,
because it doesn't tell you anything about how, when, or why to use it.

Still is a complex temporal quantifier, and refers to temporal continuity from past to present.
Like most quantifiers, it can appear either directly before the constituent it binds (in this case
the constituent some time left), or before any constituent that contains that (in this case the
verb phrase be some time left).

So they're both fine. In this case.
In both speech and writing (anything that works in speech is OK in writing).
Other kinds of adverbs have other rules governing their placement.