How many times on the same journey is an inspector allowed to ask to see your rail ticket ?

They are usually only allowed to ask one person each once for their ticket, that doesn't mean they won't ask again, you can choose if you want to show them or not but that choice not to may result in consequences.

An authorised official is permitted to ask to inspect your ticket as often as he/she likes. It's part of the conditions that you accept on travelling

As many times as he would like.

100 but I am sure he was asking to see something else.?

There isn't a limit. You probably look like someone who would try and cheat the system. 

They probably ask after each stop. Just keep your ticket handy. 

Lick the back of the ticket and stick it to your forehead - problem solved. 

They can ask you as many times as they want to.

Twelfty. After that you can stamp on his foot.

Simple answer: As many times as they like. You are obligated to show a valid ticket.