Yes but very slowly. I don't think you need to worry about it so long as the storage location doesn't have big temperature or humidity swings.
Electrolytic Caps are a problem - they should be powered regularly. If you store them for several years then when you power up (if unlucky) BANG!! You have an exploded cap. I won't go into the details but there is a simple procedure to reform them BEFORE you power up gear that has been in storage for a long time.
Yes. Some electrolytic capacitors may be shorted, even if the amp is idle for as little as six months, depending how old they are. What happens is that a thin layer of aluminum oxide insulating the foil deteriorates and the cap shorts out. This insulating layer can be reformed by applying a low voltage across the cap in increments up to its rated voltage.
The best way to do it is to call the manufacturer and ask what should be done if the amp was idle for more than a few months (or whatever time frame you're concerned with). The other thing that can be done is to plug the amp into a variac, start at 10 volts and work up to the wall voltage (120, 240, etc) in 10 volt increments each hour. This is FYI - I am not assuring that no damage would occur to any particular amp because there's no telling if the cap reformed. You can only know this by using certain commercial test instruments (an easily home-made one works) or hope for the best by not hearing a bang. But as always, ask the mfr before you try anything like this.
Gs5556 - I suspected it has something to do with overvoltage. I read somwhere about hydrogen release (and explosion) in dry aluminium electrolytic caps.
On the other hand datasheet of the few brands I checked show shelf life only 1/2 of load life and my company uses sometimes in production (special orders) very old caps stored for few years and everything is fine. They shouldn't but we don't have system to trace "perishables".
Could the difference be caused by extreme working condition in many high power amps like high ripple current or voltage close to rated for the cap?
You can buy variacs... just about anywhere (that sells electronic items, that is). In its simplest form, it's a wall-wart with a multiposition switch on it indicating different output voltages per position... You just need the appropriate variac (i.e. TALK to a sales tech)
Make sure you don't reach HIGHER voltage than the caps indicate (70? 80? V).
HOWEVER, I strongly suggest you get a TECHNICIAN to do this.