life span/failure rate of filter capacitors?

Depends on a lot of variables, size of the capacitor (larger caps don't get hot as quickly as small caps) if it's placed near hot areas of the amp and quality of the capacitor. Most of the really large caps of high quality usually last a lot longer than all the smaller caps in an amp.

Eric has provided good advice.  Plus you may also begin to hear fluctuations in the music with power capacitors.  If you are in the NYC area I can take a look at your unit.  On Parts Connexion look for Nichicon Super Through parts.  You can go up in value if you have to just make sure that they fit in the space you unit has.

Much has to do is how much demand on them in the circuit ,better to have more smaller caps lower distortion ,  how hot is the area and how much use .

failure much higher in amplifiers ,quality too of the caps has a lot to do with it . 
caps get dried out as they age .

Eric has provided good advice. Plus you may also begin to hear fluctuations in the music with power capacitors. If you are in the NYC area I can take a look at your unit. On Parts Connexion look for Nichicon Super Through parts. You can go up in value if you have to just make sure that they fit in the space you unit has.

Thanks, @bigkidz , I just did a search at PartsConnexion for Nichicon Super Through Electrolytic caps, and surprisingly they came up then when they had not came up before. However, not the value that I believe are in there presently (560uf 400v).

As far as @erik_squires ’ advice, this amp is a 2001 model, and I did have the bottom off two years ago to change the signal caps and at the time I was looking at and checking the values of everything I could (because it was a biasing issue that I was trying to fix) and those large filter caps appeared good from a totally visual perspective, and I remember that with a cheap Chinese capacitor checker from Amazon, they tested within parameters.

It was just that thread I pasted above that got my ruminating on this. And I am curious about this: I took this amp out of service in 2010 and didn’t put it back in action until quite late in 2017. (And for a couple of years prior to 2010 I barely, if ever, used it.) Should I look at these caps as 21 year old filter caps, or as 14 year old caps?

I am in Pa., in the Pitt area, btw.

Thanks.

It's  a lottery, but 20 years is good going. That said, I have a pair of Meridian active speakers in my garage that are still working 35 years on. It kind of depends on whether you believe in preventative maintenance or are a kind of fix it when it breaks person.