I recommend checking the wiring; make sure the connections are tight. If the battery does not take a charge during mowing then either the battery or the charging system is defective. The easiest way to check is by disconnecting the battery and charging it with a battery charger or trickle charger. If it charges then the alternator and/or charging circuitry are probably at fault. If the battery charges during normal use but loses charge overnight then there are again two possibilities, either the battery is defective or there is some sort of electrical short in your mower that is draining the battery overnight. When the battery is fully charged, disconnect it and let the battery sit overnight. In the morning reconnect the battery and try to start the mower. If the battery is dead then that is the problem but if the mower turns over then probably there is a short in your mower somewhere.
You could have a bad alternator, regulator, operator presence relay, or a broken wire in the wiring harness of the tractor.
Go to the regulator on the engine and disconnect the 2 white or yellow wires. Start the engine and set it at full throttle. Measure the voltage across the 2 white or yellow wires you disconnected from the regulator. You should measure 28 volts ac or more. If you measure less than 28 volts ac, the alternator on the engine is bad.
If you have the correct voltage, go to the relay that has 1 black, 1 blue, and 2 red wires to it. With the engine still running at full throttle and the wires connected to the relay, measure from each red wire to a good clean ground. The voltage should be the same on both wires. If the voltage is more on one red wire than the other, replace the relay. If you have the same reading on both red wires, you have a bad regulator.
This can be an extremely hard issue to track down. I highly recommend calling a service professional to diagnose and repair your mower. If you do not feel confident repairing this problem yourself, then you can have it repaired at your home by a Sears technician. Here is a link for the website:
Sears Home Services