yes it does go off as it absorbs moisture from the atmosphere. This can then crease issues with corrosion in the system and this is often why its advisable to swap it out on your car every couple of years.
It’s a bit more complex than that. DOT fluid absorbs water and the boiling point decreases. However, bike brake systems are sealed, so they actually run for years without any problems. If you’re racing DH or doing crazy descents in the alps, you would definitely flush the system with fresh fluid just to be sure, but the average rider is not really doing to have a problem unless they’ve thrown their bike into a swimming pool and left it there for a month.
Mineral oil based fluids don’t absorb water like DOT fluid. However, if water does get into the system, it will pool at the lowest point (the caliper), whereas it will end up distributed throughout the system in a DOT based system. The caliper is the only part that actually gets hot, so mineral based systems end up with the water at exactly the worst place. The claim that water is a problem for DOT, but not for mineral oil just doesn’t really have any factual basis – it’s not generally a problem for either, but if it does get into the system, it’s a bigger problem for mineral based systems.