My first thought was that maybe you use too heavy gauge strings or your action may be too high, both of which can greatly contribute to left hand fatigue in my experience because you then need actual strength to fret a note.
This. Yes. And that you may press harder than needed. Also if your frets are too low (leveled with fretboard) it's too hard to get a decent note without buzzing. The thumb behind the neck should only be used as a "doorstop". You shouldn't use force on the thumb to meet your fingers on the opposite side. Do a test like this:
A. Release the thumb completely behind the neck.
B. If you fret with any finger on the other side, and fret, do you have to press so hard before a note gets heard that you are moving the whole neck and body in and out?
Does it wiggle or bounce? Bounce is what I mean that the bass goes back into a place it had before you did fret/press anything? You should press the frets/strings as much as needed, not more. Use just as much pressure that is needed, not more. Do this slowly, and think how much you really need to press before the note becomes "un-buzzy", i e a clear note. Then, hone it in, and woodshed, so you don't ever again use more force than needed. Pressing too hard makes the note go out of pitch too.
C. Then your tension, of strings are too strong, and too stiff, and you'd better check on ALL things first, like already mentioned:
1. String gauge. Go down to super slinky flubby 030s.
2. Action, string height plus relief? Must be adjusted accordingly and with great accuracy.
3. Fret height? Are the frets tall enough? because if not, you have to use excessive force to keep the string down. Especially at the first few frets. A refret can turn out expensive. But considering the cost of artrithis, carpal tunnel, pain in your fretting hand, and the medicals and visits to physiotherapists, it's very little in comparison.
4. Thumb behind the neck. Be vigilant and wary. Constant monitoring.
5. Angle of the neck/bass to your body while playing. Check it out, adjust strap to see if it becomes better or worse by raising it or lowering it.
6. Some won't believe this, but heavy NECK DIVE instruments may cause your fretting hand to keep the neck up all of the time, weighing down on your hand. Fatiguing in the long run. This is something most people don't detect at all, and think it's part and parcel of playing bass. Or any instrument. It's not.
I agreee totally, with the rest of the posters, something's wrong along the line.
If all else above have been seen to and checked out by professional setup repairman, then you just play too much and have to rest ever so often. Don't ever play through pain! Never Ever!
Here's a picture. Is the pain worse or better when alternating thumb behind the neck and thumb over the neck like in this pic?: