3rd Gen Macbook pro randomly suspends My 3rd Gen (late 2013) MBP randomly suspends.

I've already seen this and this and this and this. And unfortunately, none of them quite match what's happening to me.

I will be in the middle of working on my MBP and it will randomly suspend so I have to hit the power button to wake. Pressing the power button resumes from suspend but then it will do it again within a few seconds of use unless I plug it in. Does not seem to necessarily be tied to the remaining battery life (happens more often &lt; 40% but it's happened at 68% and I've gotten down to 5% as recently as this week without seeing the problem).

This is a core i7 machine with 16 GB RAM and a 500 GB SSD. Coconut battery reports that I still have 75%+ of the original battery capacity left. This is a machine that otherwise has plenty of life left in it if I can get this resolved.

Any ideas what could be wrong?
Your battery is dying.  It's time to replace it.
You have very similar symptoms to the issue in this other post Fully charged MacBook Air turns off when power cord removed, but the major difference is that you have enough &quot;juice&quot; to allow macOS to suspend rather than just turn off all at once.
One of the biggest factors in batteries dying is it's age.  This is a 2013 MacBook Pro, so it's got 6 years on it.  The average lifepan of a battery is 3 to 5 years so (some last only 2 while some go 6 or 7), you're outside it's usable life.
Battery utilities
Coconut Battery, et. al. are neat little tools, however, they can only give a point-in-time calculation of your battery's heath.  It does it by measuring the current (volts and amps) and the current draw.  What it can't do is measure the charge like a fuel gauge in your car.
This is why you're seeing the (confusing and conflicting) &quot;battery's ok but system sleeps when not plugged in&quot; symptom.