It looks as if this code will not terminate until "replaceTaskFinished" is set to true (which supposedly happens in replaceTaskThread). So you haven't really an independent thread here.
Also, if "replaceTaskFinished" is an instance variable, then this code is not thread-safe. Any write access to instance variables needs to be synchronized. But, as pointed out above, the code should not wait for it to become true to begin with.
Ping & DNS - updated with new look and Ping home screen widget
Hardly surprising since (as near as I can tell) you are holding on to the thread that is handling the request that started the whole thing. You should let that request terminate normally with something like a "working" HTML page and find another way to update the user. There have been a lot of discussions of this sort of thing on the ranch so do some searches.