After about 35 minutes.
Here're my notes:
"1 minute and 46.2 seconds to land the chopper (split at when I saw him begin to leave the chopper). He was caught for a bit and my walking a bit finally made him move again. For a little over 21 seconds later, he stayed on screen, walking, before going beyond a corner and out of my line of sight. Timer started when I sent the command to confirm calling the homie. I'm not touching the chopper. I'm afraid that the existence of the chopper will mean that the helicopter homie won't respawn. I'll check at 5 minutes. As I tried to get a car to stand beside for the radio, the chopper despawned. I stay on foot in case it's similar to survival calls. Helicopter homie hasn't respawned after five minutes. About 5 seconds lost in phone. Checking again at 6 minutes (timer, not adjusted). 4.8 seconds lost from the second check. I'll check again at 10 minutes. I think chopper despawned at 3 minutes, approximately. I called the chopper just outside of the first crib (apartment of Shaundi's ex). 5.8 seconds lost on 10 minute check. About 3 seconds lost on minimum bandwidth warning. Empty 15:20, lost maybe another 3-4 seconds. Lost 5.6 seconds at 20:10. 4 seconds off from 25:00 check. 4 seconds off from 30:10 check. 4.8 seconds off from 35:20 check. Ooh, respawned a little before 40:05.3. Math: 60*40+5.3-(60+46.2)-21-5-4.8-5.8-3-3.5-5.6-4-4-4.8 = 2237.6 seconds = 37.29¯3 minutes. The number changes depending on stuff like if cooldown only begins when chopper despawns, cut around 3 minutes, if cooldown only begins when homie despawns, cut about 10 seconds, if cooldown only begins when homie leaves chopper, if cooldown begins right after phone closes from call, etc.."
In terms of fixing the homie if it's glitched such that they never respawn, you must have another player call the homie for you. Otherwise, the Homie article on the Saints Row Wiki suggests altering the game files.