Put your finger on the regulator when it locks (or even when its runniing normally) - i'll put money that its very hot and that's what's causing it...
I too have a UNO running 24x7 with nearly all of the memory full and it works fine. given that the on board regulators are linear, try powering the project off a 7v plug in supply (Available from Maplin or Radio Shack)
Courty