Diagnosis
This is almost always the 'Minimum Compressor Run Time' and 'Cool Dissipation Time' settings being too aggressive. The ecobee's default settings can be too short for some older or larger AC systems, causing them to turn on and off rapidly.
How to Fix It
On the thermostat, go to Settings > Installation Settings > Thresholds. Increase the 'Minimum Compressor Run Time' from the default (often 5 minutes) to 10 minutes. Also, increase the 'Cool Dissipation Time' to 60 seconds. This forces the system to run longer and wait longer between cycles, protecting your compressor.
If That Didn't Work
The issue might be with the ecobee's temperature sampling rate. Go to the same Thresholds menu and increase the 'Compressor Cycle Rate' from the default (usually 3 cycles per hour) to 2 or even 1. This makes the thermostat less 'jumpy'.
Heads Up
Short cycling can also be a sign of an oversized AC unit or a refrigerant issue. If adjusting these thresholds doesn't solve it, the problem might be with your HVAC equipment, not the thermostat.