Might be too late for a reply, but I just joined. I don't have that problem, but, there is a couple very good videos of rebuilding the Hydro-Gear ZT-2200 which is the hydros our mowers have. They do have a filter, but it is internal. One of the videos had that very same issue. It drove fine until it ran for awhile, and that is because the oil thins as it heats up and started blowing by the pump pistons. His issue was the pump housing being aluminum and the pistons being steel, they wore groves in the housing letting oil blow past so would loose pressure once the oil heats up and thins. That part is about $130, for it and the seal kits, but it will save you $600 for a whole new unit. Rebuild seems very straight forward assuming you have mechanical aptitude, you shouldn't have a problem opening it up. His was on a Toro I think, but most consumer ZTRs have the same hydro as ours does. Just search "Hydro-Gear TZ-2200" on Youtube, and you will find a lot of videos on it.
