Hull degradation is a problem long term though. I forget the name of the process, but an enviroment such as the one that exists in space eats away at the molecular structure of everything. I remember reading somewhere that after 20 years of flight most of Voyager 2's hull was less than paper thin and the slightest pressure, even something as light a hand brushing against it would cause the entire structure to fall apart. That's not really a problem on a ship with several feet of hull. But who knows how long the GTVA built them for, I mean destroyers are a massive investment. Probably something on the order of the GDP of some modern first-world countries.
As far as food goes, with freeze-drying, you could probably cruise for maybe a month.
3 x 10,000 = 30,000 meals per day
A freezedried meal weighs maybe 3oz.; there are 16oz in a lb.
30,000x4=90,000oz and 90,000/4 =22,500 lbs of food per day
and there are 30 days in the average month
22,500 x 30 = 675000 lbs or 337.5 short tons of food consumed every month.
The average destroyer probably has a dozen consumables depots
337.5/12 = 28.125 tons per depot
That is a lot of food, but there are a lot of operations we never see., waste disposal for instance. Liquid waste can be recycled, but solid waste would have to be stored until an appropriate time. *pictures a surprised shivan flying though a cloud of crap after a wayward shot puncured waste facility 5*