Is there a term for when just by saying that something is broken and showing it to someone fixes the issue?

In my office we call this a proximity fix, as the only thing necessary to fix the issue is to be near it: we stand behind the user and everything magically works. These days we can remotely control workstations, but still the fault disappears just by the act of attempting to observe it.

They are certainly the easiest tickets to fix.

I believe what you are trying to explain is the observer effect.

In science, the term observer effect refers to changes that the act of observation will make on a phenomenon being observed. This is often the result of instruments that, by necessity, alter the state of what they measure in some manner.

http://en.wikipedia.org/wiki/Observer_effect_%28physics%29

This certainly warrants the expansion of - @#+$! I had it right here. Where did it go?

The vanishing act:

to go away, usually because you do not want to do something or meet someone:

Surely the problem doesn't want to meet anyone who can solve it. That's why it hangs around me, right!?