2000 Toyota Corolla--Power loss after 6 minutes of driving

Over the last several months, my 2000 Toyota Corolla has started losing power on a fairly predictable schedule. Like clockwork, it happens after 6 minutes of driving when the car has been sitting for an extended period of time (such as overnight) and I drive it completely cold. If I let the car warm up for 6+ minutes, the same problem still might occur, it just happens at an unpredictable time, but generally within a few minutes of actual driving. Once I have been driving the car for a while (at least 20 minutes), it is much less likely to happen.

The loss of power lasts about 5-10 seconds, just long enough to cause me serious panic at busy intersections. The loss of power is noticeable and deliberate–sometimes it is just a strong stutter/jolting action, very similar to what might happen when not shifting smoothly on a manual transmission, but more and more frequently it has been a full on stop–like the car ran out of gas, except that the engine is still running.

I have temporarily found fixes around the issue by doing things such as revving my engine at stoplights, and letting it warm up as long as possible before driving as often as I can.

I have had it looked at by a mechanic at the dealership, but they could not diagnose the problem, as it does not usually happen once the car has been fully warmed up. The car is a manual transmission with about 110,000 miles on it, and I have the oil, fluids, etc. changed regularly. Up until the last few months, it has been reliable, and any problems have been minor and easily fixed.

Does anyone have any idea what the cause of the problem might be? And if so, what would be a reasonable estimate for getting it fixed?