I dont think its unreasonable to try every 3 months but 6 at least allows you some room to show usage and history. Plus if your score increases better chances yet. Its just with Sync , one never really knows when they habe a headache and want to cure it with the blue medicine
@Anonymous wrote:
I've already called Synchrony's backdoor number to increase limits on a few of my cards successfully. Question is, how long should I wait in between requests? I feel like doing it too often will get me flagged and have accounts closed or limit decreases.
I know most people will say 6 months, but I've also heard 3. Is 3 acceptable? I'm not going crazy and trying all of my cards every 3 months, I just wanna increase my most active ones.
Thanks!
There's really no set answer to your question... all anybody here can really do is speculate and tell you what we "think". 
With that in mind, I think you have the right idea. In the past, people would call multiple times even in the same day to get CLIs on their Synchrony cards, but I personally wouldn't advise that at this time (not that it was ever a fantastic idea to begin with).
I think (there I go... LOL) that the problems a number of people have had with Synchrony were primarily due to a quick run up of Synchrony credit exposure, not so much with frequent calls to Credit Solutions. This is possibly why folks who had never called CS but who had acquired a number of new Synchrony accounts were impacted along with the folks who had been seeking multiple CLIs. This is just my own take on the data points... others might have different opinions.
In any case, slow-and-steady seems to work, and it seems like you've got a good plan.