Does the backing on bath mats last longer if they are washed
It's been at least 10 years since I tried to wash a bath mat in a top loader... so I don't know, but I suspect that a front loader is less wear and tear on a bath mat.
I have found the following in the front loader:
I only use a mild liquid detergent. Powdered detergents are generally too harsh and can degrade the rubber backing. I also use warm, not hot, water temps.
I also look for mats with better quality backing. Natural latex backings don't seem to last too long, and they tend to deteriorate even if not washed from exposure to the oxygen in the atmosphere. The most durable backing seems to be the very thin coating on some bamboo fiber mats I got a while back. But these mats also are very floppy and easily kicked up so I don't use them in traffic areas. For traffic areas I use woven 3x5 throw rugs, which are polyolefin and seem to have very durable backing. Even so, the backing tends to come off a bit in the dryer, so I usually line dry them, weather permitting. I use these throw rugs by the bathroom sink, under the cat litter box (yes, it's in the master bath, the cats prefer it that way), by the bed, etc. They wash just fine in the Neptune FL, three at a time seems to be the max load.
The memory foam bath mats are all synthetic and the backing seems not to be bothered by the washer or the dryer.