My 46 lb thrust foot controlled motorguide has decided it will only work for about 20 minutes.  What is the cause of this?  How can I fix it while on a tight budget?

I would guess it's the battery. Seems like it's not holding a charge.

is there a test I can use to check the battery? Would the battery test kit at autozone be able to detect that?

They can do a load test or you can see what your voltage is when the trolling motor quits working. you know your charger may not be working right either.

You can check the specific gravity with a cheap hydrometer.  If you don't own one then you should buy one.  When the battery is fully charged it will show 12.7 volts.

The load test is usually done free at auto parts stores.  You probably should have both done.

Jig Man, the specific gravity of a charged battery is about 1.26> when measured with a hydrometer. You will need a voltmeter to check for  the 12.7 volts.

go to any parts store and they will test it for free.

The specific gravity of a good, fully charged battery can be 1.260 to 1.300, depending on the make of battery and what electrolite they used. All cells should also read very close to the same.

If the battery does not have caps, you need to fully charge it, let it sit for 24 hours after charging and then have it checked at a local parts store or battery dealer that has a Midtronics tester and load tester

If the motor is gradually slowing down, I would look at the battery.  If the motor is just cutting off, I would replace the circuit breaker with a 45 - 50 amp breaker and make sure all connections are clean and tight.