Slow-running MacBook Pro A1297 keeps turning on and off

The model A1297 describes five 17" MBPs released in 2009-2011. Those Macs are obsolete by all measure.

There are many things that might cause the laptop to be shutting itself off and rebooting, including software corruption and hardware failure. That Mac wants to retire and you should let it.

I would suspect the hdd to be failing and/or the power supply. If the startup drive is the original that the laptop shipped with, it is very likely to be failing after fifteen (!) years. Of course, it could be something else entirely.

Still, there are a few things you can try.

Reset the NVRAM

How to Reset NVRAM / PRAM on your Mac - Apple Support

Reset the SMC.

The SMC is responsible for managing power on your Mac. Resetting it can resolve certain uncommon issues related to power or thermal management. How to Reset the SMC of your Mac - Apple Support

Does this happen on battery, wall power, or both? That can may a big difference in how to approach this.

2009-2012 Macbook Pros were prone to worn hard drive data cables. The cable is actually a super-thin and flexible printed circuit board, with minimal insulation. After years of normal use and transport, the cable insulation becomes chafed from rubbing against sharp metal edges over which it is routed, and can short out intermittently.

Cable wear is very difficult to detect by visual inspection. Fortunately, a replacement cable should cost less than US$20 and can be changed at home in about 30 minutes by a novice user. Just remember to disconnect the battery cable before doing any mucking about amongst the squshiy bits.

If you are willing to risk $20, there's a chance that could sort ot the problem. Based on posts here over the years, a worn cable can present as a litany of really off-the-wall symptoms.