iPhone’s WiFi periodically sleeps and disconnects from WiFi when the screen is locked.
iPad’s hotspot SSID is not visible when its screen is locked.
The combination of this means your iPhone keeps dropping the connection when it’s in your pocket, and you have to turn on iPad’s screen to reinitiate the WiFi connection. Not a good idea.
Now I’m using iPhone tethered through T-Mobile Android phone, till I get the SIM card from Straight Talk. It should sound like the stupidest thing you can do with an iPhone, but because Android’s hotspot advertises its SSID all the time, the connection gets reinitiated immediately, and works much better.
What’s even more sad, is that the bandwidth speed isn’t as bad as AT&T’s “4G”, even with T-Mobile’s 3G (of course much slower than the new iPad’s blazingly fast 4G LTE).
UPDATE: as mentioned in the post, there’s a hack/workaround to let iPhone not going to “deep sleep” and hence keep the wifi connection alive: playing music. I cached lots of music files via iTunes match and play all the music while on the move. It’s silly but it seems to work very well, and doesn’t drain battery as much.