The re-capping perception for ML amps is strong enough that it directly affects their resale value. I had a pair of 334s myself, and found this out the hard way when I sold them. Some non-trivial fraction of the ML 300 series amps have had caps that failed, that's a fact. Most of them are in the 331-332-333 series, though there are some cases, fewer of them it seems, in the later 334-335-366 models. This might be just because of age.
I talked to Levinson about my amps, which were from 1999, and they told me that the caps were spec'd to have a 20 year lifespan. Of course, that probably means there will be some failures due to age after 10 years, and by 15 years it would be much more visible. Lots of these 3xx amps are now 20 years old. Levinson also told me that "recreational" re-capping is not recommended or necessary, and that most 3xx amps won't need new caps until they are more than 20 years old. I'm not sure I believe them, because as caps age they lose their energy storage capability gradually over time. It's not a simple failure or ok scenario.
Capacitors, especially the soda can sized things in older Levinson amps (and Thresholds, Krell, etc), do indeed age and eventually need replacement. Both environmental and usage factors can affect aging, and it's always been my suspicion that older high-end amps have a usage model that these high-power capacitors weren't designed for. Specifically, most audiophiles turn their amps on and off, because these amps idle at 100-300 watts even in Class AB mode. The high-end audio industry is using off-the-shelf caps, and most high power caps are designed for equipment that is never turned off, like computers and telecom equipment. When you turn on those 334s what happens? Levinson didn't use soft-start circuitry, so all of the lights in the house dim as a huge, 50+amp transient of current charges those caps. It's just my conjecture, but I'm guessing that surge performed a couple of hundred times per year for ten years could prematurely age the caps that weren't designed for that usage model.
Many of the latest high-power amps use a soft start function that charges the caps over ten seconds or more. Conceived for multichannel amps to prevent tripping circuit breakers, I also suspect these soft start functions improve cap life. Finally, most amp manufacturers are now using arrays of smaller capacitors to achieve the same energy storage as a couple of big ones, and smaller caps seem to age better than large ones. (Though my understanding is that the cap arrays are really intended to lower the series resistance the output stage sees, making the power supply faster. I've never heard of aging as a design criteria.)
There's a guy on audiogon who sells replacement upgraded caps for $745 for each amp, and factoring in labor to disassemble and reassemble one of those monsters means that $1K seems reasonable.
The only way to tell if your amp really needs re-capping is to have it bench tested, preferably at rated power into 4 ohms. It might be a bit of a trick finding someone who can do that without shipping them somewhere.
