DIAGNOSIS The thermostat is sending the signal, but your HVAC equipment isn't responding. This is usually a wiring or equipment issue, not a thermostat bug.
FIX Go to the thermostat's Installer Test mode. On the device, go to Menu > Settings > Advanced Settings > Installer Setup (code 4114) > Test Equipment. Run the test for your heat or cool. Listen closely at your furnace or outdoor AC unit. If you hear a click from the thermostat but nothing happens at the equipment, the wiring connection at either end is likely loose or the control board fuse is blown.
IF THAT DIDN'T WORK If the test runs the equipment fine, but normal operation doesn't, there's a good chance your system's safety limit switch (like a flame sensor or high-limit switch) is tripped or dirty, causing the equipment to shut down shortly after the thermostat calls for it. That's an HVAC service call.
HEADS UP The "equipment running" message just means the T9 is outputting 24V on the relevant wire (W for heat, Y for cool). It has no way of knowing if your actual burner or compressor kicked on.