I did some minimal research on the OG&E site last night while at work (hey, I'm in the power industry, just not THAT company). Couldn't pull a lot of information out of their web site, though they do show maps where "upgrades" are taking place, as well as tree trimming. Typically, mishaps, whether man-made or natural, tend to blink entire circuits, and not just part of your service.
In most areas, the 120/240 service is drawn from a single phase, one hot primary wire and a ground, so losing part of your service seems pretty improbable at that level. That is, out on the lines up to and including the pole-top (or underground) transformer, there isn't typically a means of cutting off part of a customer's service, at least not deliberately, and certainly not across a wide area like that.
I mentioned smart meters - even the meter, in itself, typically isn't able to do this, but it might - there is some logic in the meter that could automate meter reading, and might have some controllable functions like cutting off one leg of the 120-240 service, which would essentially cut off roughly half of your home's circuits and would probably shut down any 240 volt appliances (like the AC). This is NOT a good approach for load control, if that's what they're doing.
Either all off, or selecting appliances, which I doubt you've given them the control to do, is the best approach. I wonder if they have a new system that isn't working correctly, that is tied into their new "smart grid" technology and possibly new smart meters. And honestly, I don't know 100% if a smart meter by itself, is capable of cutting off any power. Mine isn't, but it does provide automatic meter reading, and it sends data to the power provider when the lights blink - this IS part of our "smart grid", whereby the power outage footprint is determined quickly and automatically for the automatic system and for the customer service/dispatching folks at the main control center.
The smart grid does allow for systematically cutting power to blocks of customers using pole-top circuit breakers (often called "reclosers") and, of course, the old tried-and-true method of just opening the circuit breakers at the substation either by remote or by operator intervention. That would be part of a rolling blackout, and if they were doing this deliberately, there would be some notification or news releases stating as such.
I would get hold of OG&E and let them now what's happening, and that you're not the only customer that's dealing with the issue. It shouldn't be happening IMHO.
Many thanks, meyer — it’s certainly worth a try. People here are already pissed off about OG&E advising recently that they were going to jack up rates AGAIN by another few bucks a month, starting immediately. I’d think they might be reluctant to infuriate their customers even more than they already are. So, there may be a decent chance of success in doing as you suggested. Will update with results. Hope to be able to make a few calls early next week.