Most likely you've got a loose connection somewhere, either at the outlet itself or where the circuit connects at the breaker panel. When an AC unit draws a big power load, it heats things up slightly, and if there's already a loose connection, that heat makes the resistance worse - the contact gets even worse temporarily, then cools down and works again. This cycle repeats. The fact that the breaker isn't tripping is actually a red flag for this scenario; a truly overloaded circuit would trip eventually, but a loose connection just causes intermittent problems.
Start by turning off power to that outlet and unscrewing it from the wall to check if the wire terminals are tight. Sometimes installers or previous work can jostle connections loose. If the wires look fine there, the issue is likely at the breaker panel itself - the wire connection where it attaches to the breaker might be loose. You really shouldn't mess with the breaker panel yourself if you're not comfortable; call a licensed electrician to check it. They can tighten connections and also verify whether the circuit is actually adequate for running both the AC and other devices on that same line.
Don't ignore this. Loose connections get hot and can eventually cause a fire. Get it checked soon rather than waiting for it to fail completely or cause damage.