Well, sort of.
It has been a hobby for a few people at 2ch.net[J], Japan’s biggest anonymous BBS, to show off "how long they could let their iPhone stopwatch running". On May 29th 2012, this astonishing new record was introduced to the BBS, which put those enjoying this hobby in shock.
The one who posted this screenshot commented that the counting of stopwatch freezed at the time shown above. Actually, this is a well-known computer software problem called Year 2038 problem where some software fails to work properly after its clock counts over 2,147,483,647. You can find details here.
Since I couldn’t help testing whether iPhone clock has same problem, I tried to set my iPhone clock at year 2038, but counldn’t. The date selection after January 1st, 2038 was grayed out. It might be the messege from Apple saying "Don’t mess with it or worry about it. There is plenty of time to fix this".
Haruo Nakayama