"I need a way to detect this."

Welcome to the "halting problem". (Life patterns are general computers and hence determining their termination falls under the halting problem).

There's no general way to detect these loops -- While two-stage cycles are quite common, you can get three stage... and four stage...

In fact you get N length cycles with a probability of something around 1/N.

There are also sequences which don't repeat exactly, but also don't produce new information -- the famous "r-pentomino" settles down into a sea of static objects, blinkers and a couple of gliders. The blinkers/statics form a simple loop of 2, but the gliders are more problematic -- while they repeat their internal pattern, they move across the plane so the generations aren't identical.

The good news is that because life is forwardly deterministic, if you see ANY generation you've ever seen before, you know you've entered a loop.

So one simple approach might be to hash your array and keep the hashes. If you see one again, it's a loop.

It won't help you with the gliders... you'll have to get MUCH more creative with them. Note that there is an arbitrarily large set of moving-but-effectively-unchanged objects. Collectively they're call "spaceships" and there's a couple of dozen of them. (There's a catalogue at http://www.conwaylife.com/wiki/Spaceship)

You could measure the expansion of your life frontier (the boundary of live cells) and the count of total live cells. If it steadily increases at a linear rate for more than a certain amount of time, you could conclude that you have a looping system along with a cloud of spaceships moving away from the objects. Spaceships move at known fractions of c -- a glider is c/4 and after 4 cycles it returns to the same number of cells... The problem is that if you have (say) a 5-blinker in your static objects, your loop is now 20 generations, so what you're looking for in that system is a long-term linear trend in the boundary growing at some fraction strictly less than c while the number of cells oscillates through a set of counts (which annoyingly can also be arbitrarily long...)

To emphasise there is NO general purpose solution -- it's demonstrable mathematically for this class of systems that you cannot produce one and trying to will consume periods of time bounded only by your lifespan.

You can get a "good enough for me" solution so aim for that.