Tim,
I have the same issue you have - I don't think most users really notice it bc most people just don't delete one by one.
I've had it since start of iOS 8, but so that you know, the issues exists beyond the Recent Calls screen. It also exists on any kind of 'list-like' screen where the swipe from right to left deletes (except on emails - because emails delete in one swoop operation [if you have it setup to not confirm deletions as I do]). Most specifically, I dealt with that issue over and over when deleting the myriad of duplicate keyboard shortcuts that had been created under the iOS 8 environment [that's completely separate issue where many of my shortcuts would show duplicated and I would delete them over and over and they would re-appear after a few days or after restarting the phone].
Anywho, yes, after you swipe a few times the delete stops working and instead, the swipe acts as a 'selection or click' action - so in the recent's call tab, it would actually cause you to dial the number; in the shortcuts tab, it would cause the selection of that shortcut for edit.
I did find a little trick to get around it: the thing is that the screen needs to 'scroll' in order for the swipe to delete feature to not become disabled. Thus, instead of trying to deleting one entry after the next, I would do a 'small manual scroll up and down' on the screen before doing the next delete - sounds silly, but when you need to delete about 100 shortcuts, you have to find workarounds, lol.
Anywho, I just checked that the new update to 8.3 did NOT fix this swipe to delete issue and the only reason I felt compelled to post about it is because with 8.3, Apple seemed to finally start to fix the myriad of issues out there, so I figured, maybe if I report this one, it might get fixed in the near future.
Regarding shortcuts problem I just mentioned, I gave up and created a new apple id and used an app to edit the shortcuts file from my PC iPhone backup and restored the edited file to the phone - problem solved (after many iterations). iOS 8.3 says that it fixed issues with shortcuts, but it does not specify what, plus it's too late for me now.
Good luck to us all to see when Apple decides to fix this swipe to delete issue.
Carlos..
iPhone 6+ on iOS 8.3