Can "wonder if" be followed by a subjunctive clause only?

It is correct to use the subjunctive here, and not all that uncommon. Many native speakers would also use "was". It depends somewhat on personal, regional and stylistic factors. In speech or ordinary writing, generally either sounds natural. I suppose some might find the subjunctive to sound odd or old-fashioned, or the indicative to sound inelegant or uneducated. If you want to use what native speakers would consider the most strictly "correct", as in the context of a grammar test, then it might be a safer bet to use the subjunctive. Incidentally, the past subjunctive can also be used with "whether" in similar circumstances (hat tip to tchrist in comments).

Here's a Google ngram chart for "wonder if she were" and "wonder if he were". If you look through the citations, you can find examples of these phrases being used by other English writers in comparable contexts to the ones cited in the question.

As shown by Google Books

"wondering if she were still" About 25,800 results

this is a well established use of the subjunctive, and still in use.

The reason for its existence lies in the on-the-fly introduction and support of doubts as to the reality of the situation/assumption, in concert with "wondering" and emphasizing it, something that could be rendered correctly only in more verbose phrasings, also pertaining to subjunctive mood in nature:

"wondering if she might still be a maiden"

Certainly "was" /can be/is/ used instead, but this effect of /emphasizing/raising to power/ the wonderment goes out the window, and you have at work what I, at least, would call mentally flatter writing :-)

About 25,800 results

I agree with both you and Martin, more or less. The quoted examples seem fine, to me, but then they are also fine if changed to the indicative. But more importantly (and why I decided to write an answer), I think you're on to something interesting here when you note:

Also, I believe that using Martin's structure in the present tense may sound even more wrong: "he wonders if he be dying" (present subjunctive)...

This example in the present tense is really bad in current English, and I find all Martin's examples unacceptable if they are changed to the present tense.