I shall be going through Jeddah on my way from Frankfurt to New Delhi, and have a stopover time of 11 hours 40 minutes, which is less than the stipulated TWOV time of 12 hours. Do I need a transit Visa? If the latter flight is delayed, will the airlines company manage the trouble?
Of course you don't need a visa. If 12 hours is the max, it's 12 hours, and you're staying for less, period.
This rule is for the airlines to enforce, not Saudi immigration (as you won't be dealing with Saudi immigration). So if anything happens to the connecting flight, you still will have no problems.