In principle peltier elements should be very robust over time, as a solid state system where the only moving parts are fans (versus traditional refrigeration which includes a high pressure pump...).

In practice I strongly suspect most peltier based systems are built very cheaply... because their inefficiency means the majority of the market is bordering on a scam. Sophisticated consumers aren't going to be buying very many fridges built with them (of course you might have a niche use case where they actually make sense and you're willing to pay for a quality product, but do most purchasers?).

Thermal cycles is murder on rigid electronic connections; the mechanical connection between the heatsink on each side of the peltier cell being a prime example.