Finding a Water Leak

Does your water pump cycle by itself sometimes?
If it does check that the water supply to the back of the toilet isn’t leaking !

Take it to a Sealtech shop and have it pressure tested.
https://rvleaks.com/testing-locations/

After you get through checking the obvious I suggest you spend a $100 and have the rig pressure tested. Finding leaks is a PIA and often the source of the leak is far from where the water settles.

Also if there are any windows above the area check the seal around the windows. Mine had cracks in the sealant at the top of the window frame, the rain water was running down the window frame inside the wall, down the wall and exiting at the floor.

I find it very strange that we've had this camper for 7 years and haven't had any problems of this sort, but now we have the issue on both sides at the same time.

I'd take a close look at two places. The first one being where the flange for the door mounts to the side of the trailer. if it wasn't properly sealed when the trailer was built water could be leaking under the flange, running down the flange and soaking into the floor structure. The second place I'd look is under the trailer where the floor is getting soft and looking for any signs of where water could be soaking up through the underside of the floor.

Go up on the roof and closely look at anywhere you have sealant or a seam. Check for holes or punctures in the roof membrane. I suspect you have a roof leak and the water is running down the inside of the wall and saturating the floor.

This is for a travel trailer. 2010 Four Winds Lite model 252RBGS. The storage compartment is at the front of the trailer and extends from side to side with access doors on each side. As I mentioned in the original post, there is no evidence of any water either on the floor of the compartment or the walls, even after a very heavy downpour.

For storage compartments especially, water may be splashing up and in if you drive in rainy/wet conditions when it would not be able to get it while parked during a rainstorm. Check the sealing of the compartment boxes underneath (particularly if exposed) and the joint between them and the skirting and that sort of thing.

I would look first at the rubber seals around the doors. The only true way to find water leaks is with a SealTest. Professionally done will identify every place where you have a leak. Then you have a choice. Mark them all or fix them all.