If your T500 turns off on its own:

The T500 has an option to use a timer. Do you have the timer set on a certain amount of time?

How to use the timer: 
Press TIMER to have the air purifier automatically turn off in a set number of hours. Up to twelve hours.

Note: If none of the preset hours are not selected, the purifier will continue to run until you manually turn it off.

If the timer isn't the issue, try the following steps:

1. Unplug the purifier from the wall outlet.
2. Remove the power cord from the back of the purifier.
3. Remove the panel and the filter from the purifier.
4. Let the purifier rest for 30 seconds without the filter or panel installed.
5. Reinstall the filter, making sure that it is placed securely back in the unit (insert bottom of the filter first, and then press the top and secure the filter with the filter lock by rotating it clockwise. Then proceed to press on all four corners to ensure that it is completely locked in place.)
6. Place the panel back on the purifier, making sure it closes securely. 
7. Reinstall the power cord into the back of the purifier, ensuring it is tightly locked in place. 
8. Plug the purifier back into the wall.
9. Press the power button to power on the purifier.