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Depending on types of materials used, I would venture to say a vivarium will last as long as you want it to, within reason. I have heard of tanks lasting 10 years or more, but I dont think I would be able to look at the same tank for that long.
That being said, use good wood like oak or cypress to extend the life of the tank. Soil will be replenished by frog poo and dead flies and general life in the tank. However, sooner or later most soils will decompose to mush. Soil can be replaced after a few years though, as I have used the same soil in a tank for over a year with no problems. It will last longer if it is not constantly wet.
Water in the false bottom can get to LOOK nasty over time, but the general consensus is that frogs dont spend enough time in the water to cause a problem with water quality. I try to keep mine looking halfway clean and freshening it on a regular basis though. The plants in the tank will go a long way towards helping water quality.
Background? Great stuff background I dont think would decompose at all. Coco backgrounds I dont have any experience with, so I cant really comment on those.
I hope I helped. This forum is a wealth of information. Read all you can!