Such deviations from the steady tempo happen for a couple of reasons:
1. Change in texture and other musical elements
2. Change in difficulty level
In other words, when there is nothing new in a composition, an organist may play in a steady tempo, like on autopilot. But when you see a different rhythmical figures coming up or when the texture starts to become more complex then a possibility arises for the unwanted change in tempo.
Change in difficulty level is also very important - when there is an episode without pedals, we may begin to play faster and vice versa.
So how do you keep a steady tempo in such situations?
One of the biggest things you can do is to be aware of the pulse in the composition.
For example, when the organist plays an episode in the fugue without pedals and sees a difficult pedal entrance later on, at that place he/she may be concerned about not missing the right notes in the pedals. Therefore, the thought about a steady pulse is forgotten.
Being aware of the pulse is best done when counting out loud and sometimes even subdividing the beats in the measure. It's not easy to do, but if you achieve a feeling that you are playing and saying the numbers of the beats rhythmically, then your mind is really focused on the pulse.
I stress the importance of saying them out loud so that you can actually hear the words "one and two and three and four and" (in 4/4 meter). Simply saying the words silently might not be sufficient. Practice this way and no matter if you play only in 2 or 6 parts, you will always perform in a steady tempo.
You don't have to do this kind of exercise for long months. Whenever you catch yourself (either live or in recorded performance) deviate from the steady tempo, play a piece a few times with steadily counting out loud the beats and the results will be self-evident.
NOTE: By keeping a steady tempo, I don't mean you should play without any regard to important structural points in the piece and automatize your performance. It would be very boring to listen and to play this way.
P.S. Sometimes slowing down simply means that an organist can't play fluently. If that's the case, follow these tips.