Yay, it's a flying Shyft!

Is it possible to get stuck in an infinite loop with an optional ability that costs ?

No.

Are you asking "Can I activate this an infinite number of times, thus causing the game to crash?" If that's the case, then no. I can't remember what the exact rule that governs this says, but it's something like "If you can do something repeatedly for as long and often you want, you can just state how long and often something happens, then it does, and the game continues. If a player feels that another player is intentionally wasting time, you can call over a judge, and if the judge agrees, he will issue a reasonable penalty."

Also, cards like this are why you can respond to your own abilities without passing priority. Otherwise, you'd have to legitimately ask your opponent in between each activation if they want to respond. That's not how the game operates, though, and you can just say "I put this ability on the stack 100 times. Any responses?"

I will note, however, that this is still a frustrating point in MTGO. If we were involved in a low-level tournament, and you had used up too much of your clock, I could just keep activating this thing and waiting for you to respond. The end result? I'd eat up my clock, but so would you. I'm not sure what would happen if it was an important match. The computer is a Level 3 judge... it can be overruled, but can a level 4 judge issue more time to finish a match? I assume they should be able to, but I don't know. I also wonder if you can appeal to a higher authority after the fact. The log of that match should make it obvious that one person was intentionally wasting time. Of course, as soon as you had to appeal something, MTGO failed you.

Fortunately MTGO has useful abilities like "Always yield to ability from Scintillating Spirit". If I used that, the only one whose time you'd be wasting is yourself.