I know it's probably not the answer you are looking for, but if ASIHTTPRequest is crashing then it's at least 90% likely that there's an error in your code - the most common problems all relate around request vs delegate lifetime issues. NSURLConnection might well just give you a different set of problems (though it might just work well). NSURLConnection also has a lot fewer features (no caching etc).
Generally, you need to remove the delegate from ASIHTTPRequest before the delegate is destroyed (ie. at the very start of the delegate's dealloc method). So long as this is done, there is no way for ASIHTTPRequest to call a deallocated delegate. You must do this for every request, including ones that have been cancelled.
The bug you link to seems to relate to one very particular circumstance, and at least a one reason it's not been fixed is that it appears no one else has been able to reproduce it.
(I'll caveat this with the statement that their have been problems with ASIHTTPRequest in the past - in particular the release of v1.7 contained some race conditions that could cause crashes, but these were later fixed in the git tree. I've not personally tried v1.8, but v1.7 with the fixes is working very well for me.)
It might be worth posting a new question detailing the crash you're seeing and sharing some of your code / how you use ASIHTTPRequest.