Relax.
I flew Continental Airlines during the worst years in its history (late 1980s – early 1990s), and not only was I happy with their service during those years, but they served champagne on the flight I was on when it was announced that day that Continental Airlines officially had emerged from bankruptcy.
Some of those OnePass miles were earned on Eastern Airlines.
I still have more than 150,000 OnePass miles, plus more that is currently being used for an award trip.
My PanAm miles converted into Delta Frequent Flyer miles, which I shortly after instructed Delta Air Lines to merge into my existing account.
I have enough USAirways Dividend Miles for a round-trip award ticket anywhere in the United States, including Hawaii.
I never worried about my American Airlines miles, even though they never declared bankruptcy. However, some of those miles were earned on American Airlines. Others came from Trans World Airlines, and still others came from Reno Air.
I allowed my United Airlines account to lapse years ago when there was no way to extend the expiration date of my miles, but then again I only had 400 miles left in the account anyway after I transferred them into my Hilton Honors account at an incredible promotional rate, just before many of those miles were ready to expire. If I had miles in my United account today (if it still existed), I would not worry at all.
Speaking as a veteran who has had miles in accounts from companies which either declared bankruptcy, went out of business or was acquired by another company, I have not lost one mile due to any of those factors. Do not worry! The only time I have ever lost miles was from accounts which I allowed to expire, such as United (as described above), Midwest Express and America West — none of which I had enough miles with which to do anything.