Is the Apple Care Plus subscription supposed to be ending automatically?

If you are still being charged for it, then it should still be covering the device. Make sure the Apple Care+ you are being charged for is for the MacBook Pro, and not for an other device you may own. Apple Care+ for iPhone is only for iPhone and cannot be used to cover a Mac for example.

Each device has its own independent coverage.

If you bough Apple Care+ for the MacBook Pro as a single payment, then it ends after 3 years. You can now extend it to a monthly payment for an indefinite time if you wanted to, but its something you would have had to do manually. It would not happen automatically.

You can enter the MacBook Pro's serial number at the following website to check its Apple Care+ coverage status: click here-> Check Your Service and Support Coverage - Apple Support

AppleCare is one year free , then an additional up to two years with payments spread out over the two years. I your time is up and you are still being charged. you need to get hold of Apple.AppleCare Products - Apple

<< AppleCare is one year free ... >>

That is not quite correct.

Apple provides a one year manufacturer's warranty, which covers ONLY defects in materials or workmanship.

Example: glass breakage is generally Not covered under Apple warranty, because it is generally not found to be a defect in materials or workmanship.

AppleCare PLUS covers more items, but under different terms, and if you don't sign up for AppleCare plus in the first 60 days, you can NOT sign up later.

Example: Screen replacement is covered for up to two such events in the coverage period, but a co-pay of about US$100 is required (about the cost of the labor for a screen replacement -- the Full Retail price of which can exceed US$800)

NB>> If you made the decision to NOT pay for the AppleCare PLUS extended warranty, you made a decision to bear the cost of repairs during the remainder of extended warranty period yourself.