I am confident storing my instrument tuned for two reasons:

1.) She was stored with tension on the strings for over six years between when my sister put her down and I picked her up.  The strings were horribly out of tune when I started but overall have been performing nicely since then.  (Except the E-string which I broke last fall and had to replace.  The other three are old though.) 

2.) Since they're synthetic core strings, and so can be modelled roughly as a viscoelastic material, I know that the stress on the strings will decrease over time when exposed to a constant strain (such as being stored while tuned).  Hence, the need to retune on occasion.

The real question is whether the creep that happens as a result of the constant strain of being stored while tuned would result in failure before the fatigue caused by cyclic loading, e.g. if the strings were slacked and tightened repeatedly, all else being equal.  Practically, I would say that it doesn't matter because you'll never get to that point.*  If you increase strain too quickly then the string's molecular structure is not able to rearrange itself fast enough in order to accomodate the extra energy so "pop" it goes.  The more times you relax and tighten the string, the more chances you have at over-tightening it or tightening it too quickly. 

So my vote is only mess with the strings when necessary and let them do their thing otherwise.  If you do have to mess with them then tighten gradually and steadily rather than sharply.  You want to avoid increasing strain too fast or overshooting and putting more stress on the string than the material can handle.   (Which is probably why the rule of thumb is to "tune up" to a note rather than overshoot and try to work backwards.)

Well, there you have it.  I think this is the first time anyone has ever managed to study for a materials engineering exam while procrastinating.  Any engineers out there who want to weigh in?

*general "you"