I believe this is due to mIRC being a 32-bit application (even if run on a 64-bit OS). The underlying timecounter is limited to 31 bits of data (the 32nd bit is used for signage, which plays no role with regards to a timecounter but idiot programmers of OSes and libraries chose to use a signed 32-bit number rather than unsigned), which happens to be the number of seconds between January 1st 1970 @ 00:00:00 and January 19th 2038 @ 03:14:07.

Full details are available on Wikipedia. Read (do not skim) "Solutions":

http://en.wikipedia.org/wiki/Year_2038_problem

There's no real way for mIRC to solve this other than to provide native 64-bit builds. Those of us using 32-bit OSes (regardless if our CPUs support 64-bit numbers or not -- the limitation is not there), or those running 32-bit builds of mIRC on a 64-bit OS, will just have to deal with it.