Why did the rendezvous fail?

As far as I could find, it was for dramatic effect. After doing some research into the actual mission, it appears as though the real-life mission had them purposefully going with the bombers to Berlin.

Wikipedia's Plot summation for that portion of the movie:

The Tuskegee Airmen are then tasked with escorting the first American bombers to attack Berlin. However, despite their P-51s having more than enough fuel for the trip, the 332nd is only asked to escort the bombers on the first leg of their journey due to propaganda reasons. But the fighter squadron meant to relieve the 332nd never arrives, and Easy makes the decision to stay with bombers all the way. They are then attacked by Pretty Boy, now leading a flight of revolutionary Messerschmitt Me 262 jet fighters. Despite being outclassed by the jet fighters' superior speed and 30 mm cannon, the Tuskegee Airmen are able to shoot down some of the Me 262s.

After some digging, I found that this mission was likely a mission that occurred on March 24, 1945:

The 332nd Fighter group was awarded the Presidential Unit Citation for its' longest bomber escort mission to Berlin, Germany on March 24, 1945. During this mission, the Tuskegee Airmen (then known as the 'Red Tails') destroyed three German ME-262 jet fighters and damaged five additional jet fighters.

Both descriptions mention escorting bombers to Berlin, and shooting down MS-262s. However, I couldn't find any mention that this wasn't the original mission plan all along. None of my searches returned results that indicated that there was a failed rendezvous. For example:

Tuskegee's airmen faced the best the Luftwaffe had, including the first jet fighters. On March 24, 1945, as the 332nd became one of the first Italy-based fighter unit to escort all B-17s all the way to Berlin and back, they met 25 German Me 262 jets. In the ensuing combat, three jets fell and the 332nd lost only one P-51. Significantly, the 332nd had completed the full 1,600-mile mission, for which it earned the Distinguished Unit Citation.

In fact, it looks like it would be impossible for them to have performed the mission as shown in the film. The length of the trip required their planes to have larger than normal fuel tanks to make the trip there and back. In the film, they're portrayed as simply happening to have enough fuel for a full trip. In reality, that would not have happened if they were planned to only do a partial escort of the planes. From a document that details some Tuskegee Airmen myths:

[They] needed the larger fuel tanks to take them all the way to Berlin, because all of them had aircraft over the target area on March 24, 1945.

So it must have been part of the fiction of the film.