Due to the corrective calculations being ground-based, does the reliability of WAAS degrade with increases in altitude?
Yes, but it is a fairly small error.
Some of the major sources of GPS error are able to be "corrected" by WAAS.  The WAAS stations are used to build a model to make these corrections.  These corrections are most accurate near each station, and less so the further away from each station.
A couple of the largest errors are due to Satellite clock error and ionosphere delay.  Satellite clock error is "correctable" by WAAS and will only depend on the specific satellite so would not change with receiver location.  (ie when using Satellite number 1, add 1 microsecond...).  On the other hand the ionospheric delay is somewhat location specific (when receiving satellite number 1, while standing at position X, the atmosphere is delaying the signal by Y microseconds). For locations that are not at one of the WAAS ground stations an approximation for the the ionosphere delay must be used.
However, being at altitude is probably not going to change the error by much.  I don't have data on how it scales.