Could be a number of things. Is the car running normally otherwise? Once it does get going, how does it drive once you're up to speed? Say, 55-70MPH range when cruising?

Ignoring engine performance issues (which it's possible you have) what you're describing sounds like a textbook torque converter stator one-way clutch failure. The one-way clutch inside the torque converter stator is designed to lock the stator when the difference between impeller and turbine speeds is high. This prevents the fluid from splashing back against the impeller and slowing down (or working against) the engine. Once you're cruising the stator should free-wheel, allowing the impeller and turbine to match speeds. Additionally, the torque converter lock-up clutch should engage at higher speeds which eliminates basically all of the components I described above.

If you can confirm that no engine performance issues exist, the only way of inspecting the torque converter stator is to perform a stall test (left foot hard down on the brake, right foot hard down on the gas, like you're trying to do a burnout.) The RPM should only reach a certain point (IDK what stall speed is on a civilian car but it's gotta be less than the 2700 max posted for the CVPI,) if the RPM is higher than spec, a transmission component is slipping (or you're actually doing a burnout, not the point of the test) if the RPM is low it's either an engine performance issue or a torque converter (most likely the stator) issue.

The only way to confirm a converter issue is to remove the transmission and inspect the stator support shaft. If it's in good shape, a new converter has to be installed...there's no way of opening the converter to inspect the one-way clutch.

I have seen mechanical clutches cause intermittent failure although it is rare. Sometimes they'll catch in just the right way and hold for awhile, other times they'll just slip.