How do I modify the abstract in Arxiv (without changing the paper)
The only changes that do not generate a new version number are adding a journal reference or DOI. Changing the abstract will generate a new version. As far as I am aware there are no limitations to the number of updates, but at some point arXiv will stop including udpates in the daily mailings (I believe after version 5). Making many new versions with minor changes might give the impression though that you have not carefully checked your manuscript before submitting, so generally I would recommend to save such small updates for after the paper is accepted or revised. This would also be less work for yourself and for the arXiv moderators.

Personally, in the case you mention, I would not bother to update it now. Most people are smart enough to try to remove the period at the end of the URL.