Of course, most batteries do not work as well at colder temperatures as the chemical reaction that produces the electricity is hindered by cold temperatures. Try a new battery and see what happens. It is a cheap test.

Some folks have noticed that the contacts between their cyclocomputer and the mounting gets corroded (not visually apparent) and needs some help. I have heard of people using electrode contact gel as used in hospitals for hooking up monitors to human skin. You could try that if all else fails.