Rheem heater will not "click" back on once it has reached our set temp inside the house. It shuts down and won't restart. There is a small hose connected to a small black round part that restarts the heater that won't re-engage. If I remove one end of the hose connected to the furnace, blow or slight suck in air from it the black round part makes a clicking noise and the heater will restart. I assume the fan is not sucking in air which resets and restarts the furnace.

The vacuum hose you are blowing or sucking on could have a small crack or pin hole in it,or is a loose fit,, it is necessary that none of these things happen,, take it with you to get the correct size and replace it,, is the cheapest and easiest thing to do first on your furnace

Review the sequence of operations at https://www.askmehelpdesk.com/heating-air-conditioning/heating-cooling-maintenance-repair-troubleshooting-frequently-asked-questions-58313.html

When the furnace calls for heat, the first step is for the draft inducer blower to come on. If it doesn't start up, replacing the hose won't help. If it runs, and the ignitor doesn't come on, then you need to look at the hose and switch.