What causes inability to connect for hours?

[#1]

Sometimes if I turn my modem off and turn it back on 10 minutes later I cannot connect to the internet at all, no matter what I do (even bypassing the router).  Eventually I'll just give up trying and then randomly without me doing anything it will reconnect to the internet 2-3 hours later and I'll get that green light on my router.

This happens very very rarely but obviously when it does it's really annoying. Does anyone have any idea what is exactly going on and how I could fix this in the future if it happens again?

Every time this has happened it goes the same way, nothing I do helps at all and when I give up and just wait a few hours it reconnects on its own and is fine after.

[#2]

@warpspider 

It’s called a fault with probably hundreds of potential causes. If it only occurs after switching your modem off then why on earth do you do this? The system is geared around these being left on continually.

[#3]

Definitely leave it on, but if you do want to switch it off - make sure you use the disconnect button on the router before turning the power off.
There have been times stale sessions stop a reconnection.