As a visitor you should not spend more than 6 months out of any rolling 12-month period in the UK.
Each time you enter the UK (including every time you leave to visit Europe and come back) you are essentially 'applying' for a new visa - which means you have to prove you will not spend more than 6 months in the UK, you have a return ticket back home, you have a home/job/other ties back in the US that you must return to, you have enough money to support yourself without working in the UK.
If UK immigration feel that you are trying to use the visitor visa to reside in the UK, they can refuse you entry and put you on a plane back to the US. And the more often you try to enter the UK, and the longer you try to stay each time, the more likely you will not be allowed in.
If you are refused entry, you will need to apply for a 6-month (multiple entry) visitor visa in advance of travel each time.
There is such a thing as a long-term visitor visa, valid 1, 2, 5 or 10 years, but you can still only spend 6 months at a time in the UK and they are only granted if you have a compelling reason why you HAVE to visit the UK regularly (I.e. business reasons, family you have to care for) and you already have a history of visiting for that reason. Personally, I don't know of anyone here on this forum who has successfully applied for one.
