If regeneration, spell recovery, renewal of per day abilities, etc. were also stopped due to the timeless trait, then I would be fully supportive of it also denying fast healing.
On first glance, I would say those other things do not stop. Since the traits for the plane call out specific aspects that are effected by the timeless trait.
"On planes with this trait, time still passes, but the effects of time are diminished. How the timeless trait can affect certain activities or conditions such as hunger, thirst, aging, the effects of poison, and healing varies from plane to plane."
So, time still actually passes, clocks still tick, you can sleep, and time effects things other than hunger, thirst, aging, poisons, and healing.
My reading of the
intent of the timeless trait (for what RAI and its interpretations are worth around here, anyway) is that
physical processes are suspended on the Astral Plane. That is, the physical process of aging, digestion, healing, etc. is suspended. If you had a bleeding wound, it would not continue to bleed.
Mental processes - such as the recovery of spells - are not suspended. You can still take a subjective 8 hour break to "rest" and reset your spells. X/Day abilities still renew every subjective 24 hours.
Note, however, that while time is suspended, it is still "tallied" for when you leave. If you do not eat for several subjective months, you experience no effects while on the Astral Plane. Upon leaving the Astral Plane, you will be hit by starvation, however. (see
SRD "Timeless:
On planes with this trait, time still passes, but the effects of time are diminished. How the timeless trait can affect certain activities or conditions such as hunger, thirst, aging, the effects of poison, and healing varies from plane to plane.
The danger of a timeless plane is that once one leaves such a plane for one where time flows normally, conditions such as hunger and aging do occur retroactively. ")
At the least, upon leaving the Astral Plane, if you had Fast Healing, you've got a ton of incoming regen.