Confusing Warranty question

My mom's 3GS had it's original 1 year warranty until August 11 2011.

In July 2011 it started doing ridiculous amounts of dropped calls/call failed (even after a SIM exchange) so I had it replaced. My understanding is that the new phone comes with 90 days warranty.

Now, literally 1 day before the 90 days is up the phone is completely toast, it constantly kicked itself into recovery mode and won't even restore on 4 different computers. I phoned Apple and they are mailing me out a new one...question is... Can i buy Applecare for this new replacement or am I stuck with only the 90 day warranty?

Thanks