My cth160 drives ok for about 15minutes and then dies on hill. is this a transmission problem?

Check the oil level in the transaxle gearbox between the rear wheels. Another potential issues is the oil frothing inside. The gearbox uses a swash pump which can cause frothing with the incorrect type of oil. I use a low viscosity 15/30 oil in mine (standard mineral) and it works okay. I need to top it up every so often as the axle seals are not 100%

Does this unit have hydraulic drive? If so it could be that the oil heats up and then escapes thru worn drum surfaces. I had to replace my whole transmission on my John Deere X300R because it would not go upslope after 211 hrs work. I fitted K66 transmission which needed rebuilding the rear of my machine. If you are not an engineer with complete workshop, lathe mill etc do not attempt this. Buy a mower with a decent warranty and off a company which will honor it!!