Does Skids O'Toole and the Composed talent provide for unlimited rerolls?
Let's look at the exact wording on the cards:

"Skids" O'Toole


  Whenever you roll a 1 during a test, you may reroll that die. 


Composed:


  When resolving a test, if you do not roll any 1's, you may reroll all of your dice. 


You can trigger Skids' ability whenever you roll a 1 during a test, that is apparent. 

Composed on the other hand is triggered while you are resolving the test. If you have no 1's at this point, you can choose to reroll all dice.

From the Rules Reference:


  If a Condition's effect does not list a limit, it may only be used once per instance of the triggered event. 


As this is rolling dice during a single test, you can use Skids' ability to reroll any 1's again, but you are still in the resolving the same test, and you can not trigger composed again.

To summarise:


Skids' ability can be triggered during any roll during a test
Composed can be triggered once per test


Therefore you can not roll endlessly until you succeed, but it certainly is a good combination that would lead to greater chance of success. 

There is also a discussion of this combination on BGG