In 盼还盼不来, the important grammatical part is
V 不来 wherein 不来 indicates a negative potential complement, and specifically the verb V is unfulfilled. This is one example of many possibilities e.g. 吃不完 or 想不出来 or 站不起来 or 写不下. E.g.:
Why, when I yearn, does no baby come? [approximate translation]
Similarly, in the given example, 盼不来 means what is being hoped for (as determined by the context) is unfulfilled. E.g.:
I yearn [for something determined by context], still my yearning is unfulfilled.
Note that 还 ("still") could be replaced by 也 (as in e.g. 盼也盼不来) or 都 (as in e.g. 盼都盼不来; as dan mentions) without changing the meaning (and similar things happen in other grammar structures). The 呢 in the original sentence basically expresses surprise, and it's not so important (arguably more related to a person's speaking style, and dependent on context).
I don't think
V 还 V 不来 can be considered a specific grammar structure. Negative potential complements can arise in a lot of ways:
[I] dance, [but] still don't beat this show-off.
Why do some people eat dumplings everyday, [but] still have not eaten enough?
Why, [despite] wearing glasses, [I] still cannot see clearly?
Before I was annoyed at [my] mother's nagging, [but] now I want to hear, [but] still cannot hear.
How to drink and still not get drunk?