I'm guessing these aren't interlocking mats? Are the pads separating creating gaps so that urine can get under the mats and as the horses move, the mats are slowly shifting apart?
When I was leasing a barn we had to do a bit of cheap fixes since the barn owner had a budget and we were the ones taking care of it. The stalls mats were over packed gravel which over the years, became wavy. So we got bags of contractor sand, after trying to level the packed rock (wasn't the best job) leveled them out, packed the sand as much as we could, then put the mats back over them. To keep the mats from separating/shifting when the horses moved, we placing long strips of thick rubber that you can get from tractor supply, from those mat rolls, to tighten the fit of the pads against the walls, keeping the creases in the middle tightly closed. For the 2 years we were there, that fixed the issue, and the mats never buckled, or shifted much, nor did we have a problem. Using proper amounts of bedding kept the urine from seeping.
But... when I built my own barn here on my property, I did what Avna said, put concrete in, because I never wanted to deal with that issue again. I ordered interlocking mats, then used flex seal (as per approval by the mat manufacturer), to close any change of urine getting through to the concrete. As a result, we have a perfect fit, with zero shifting, zero urine seepage, and my stalls always smell good after being cleaned. :) I also use lime dust, or PDZ on the urine spots after cleaning out the stall, to help cut down on any ammonia. My barn always smells good. :) WORTH the money to get concrete if it's in your budget!