Mohsen,
IMHO, the fuel is an absurd point to argue, as the Saudis have abundant refining capacity and there's plenty of stats a simple Google search will return proving it.
But back to the tankers, you may be on to something.
1) Availability- small fleets of unique aircraft tend to have poor availability, aka it's unlikely even under ideal conditions that all are fully mission capable. Even in the USAF, with nearly 400 tankers in inventory, ~25% are not mission ready at any given time.
2) Age- The USAF has >30 E-3s and their availability is even worse than the tankers. The "youngest" KE-3 in Saudi service is 32 years old and if USAF E-3s are having an increasingly hard time keeping their flights up, imagine what the RSAF is going through.
So, I will modify my previous comments.
As you pointed out, the early phase of the intervention show major action by the RSAF, possibly the highest tempo the RSAF has ever exercised. Dozens and dozens of sorties per day for months on straight. When you have only 5 tankers supporting likely several squadrons of combat aircraft, the wear and tear likely increased "regular" maintenance to several times that of peacetime. Something else that crops up with increased flying is inspection cycles, especially heavy or depot-level maintenance. In peacetime, aircraft can go over a year without having to go through such because such inspections on based on hours flown/time on airframe. In this scenario, what normally would take a year or more to accumulate is done is just 1-2 months of sustained high tempo flying. Once 1 of the 5 are on the ground for heavy maintenance, the pressure on the remaining aircraft increases and so begins an escalation of maintenance problems.
Under this kind of scenario, even with a decent supply chain, it's not hard to see how the fleet could become less and less available and eventually could become effectively grounded with only 2 or 3 airframes available for any operations and unable to conduct sustained high tempo for more than a week or so at a time.
Finally, you have to remember one final factor: training. In addition to any combat operations, the RSAF still has to maintain and train new KE-3 crews and also be available for F-15 pilots for refueling ops training (which, for the F-15 pilots at least, is not as intensive).
This would explain the need for USAF tankers, even to this day. The small and inadequately sized KE-3 fleet is simply incapable of dealing with this much workload.
These problems will only escalate with the continued deliveries of the new F-15SAs (84 to be delivered over the next several years)...