Re-entering the UK

There is no official limit on the number of times you can do this.

Each time you enter you may (remember the word may - you have no right to enter) be given leave to remain for up to six months. Of course if you keep doing it, the border agent may not grant you another six months on each occasion and may decide to give you only one week - or refuse you entry. You'll only know when you attempt to enter the UK.

Since I have Registered Traveler, I use the e-passport gates rather than see an agent. I know it keeps track of when I enter.....but there is no record when I leave.

Much different than Schengen.

there is no record when I leave.

There is now. There is no passport check by government officials on exit from the UK, bit since last year all transport companies are required to report passport details of all travellers exiting the UK. This was no effort for airlines, as they already kept records of passports; but it has imposed extra cost on Eurostar and Eurotunnel. For example, at London St Pancras station Eurostar employees now scan all passports of travellers before they go through French passport checks.
So the UK government does now have a computerised record of when you entered AND when you left (unless you leave by your own boat or via the land border between N. Ireland and the republic).

As a rule of thumb the UK Border Force may start to get suspicious of people using multiple entries as a way of staying for a prolonged time if they can be tracked as staying more than 6 months in any 12. This is not a hard and fast condition one way or the other though.

Even e-Passport will flag you if you trigger certain conditions, forcing you to talk to a live agent. As others have said, entry is at the discretion of the border agents.