If it's a hydrostatic trans, I imagine it's the same as my L120 and LT110. If so, it's a K46 transmission made by Tuff Torq. I've serviced both of mine, the L120 just a couple weeks ago, with fantastic results. They were both getting to where they wouldn't pull hills, then losing speed even on flat ground.
There are parts inside that are undoubtedly worn and should be replaced, but pricey. If your like me, the mower has some dents and scratches, burns a little oil, etc, an $800 transmission is pushing the limits on what you want to invest so the service was a no brainer to me. Pull the wheels, remove linkages and belt and finally the trans. On a workbench or equivalent, pull a snap ring, fan and pulley. Carefully remove the rubberish looking plug to be reused. Both of mine had cracks, which were siliconed after reinstalled. Remove the magnet underneath and flip the unit over on a 5 gallon bucket to drain. When it stops, tip it, swirl it, it will drain some more. Get all you possibly can. Tip it back over and fill it up. Recommendation is 5w-50. Several parts stores keep this in Castrol syntec. Exactly 2 quarts should fill it to the magnet that you now put back in, clean of course. Tap the lid back on, reassemble, reinstall. Low rpm forward and back for a bit to bleed everything without gaulding. Made mine like new again.
Hope it helps. Very common problem. Good luck