It is important to consider not just the current itself but also the amount of time that the current is applied. Since the motors are not 100% efficient, there is energy lost to heat. If there is too much heat, the motor will be damaged.
So, while it is no problem to run the motors at maximum current by stalling the motor for a short amount of time (a few seconds), it is not OK to stall it for a long period of time. I accidentally did this once with an EV3 medium motor and I noticed the problem after a few minutes because I could smell a burning smell coming from the motor. I have also been at LEGO conventions where motors are running all day long. Even though they are not stalled, some of the motors eventually quit working and have to be replaced.
The motors themselves do have internal protection that is supposed to cut off power to prevent overheating problems due to too much power for too long (see R7 in both the large and small motor schematics in the hardware developer kit and datasheets). But based on my experience, it doesn't seem like a good idea to completely rely on this protection.
So unfortunately, I don't have an exact answer in amps. But if you are running the motor for short periods of time with plenty of time in-between to cool down, it should be OK no matter what the current is.
For reference, these are my best guess for the data sheets for R7.