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A probationary employee has no real appeal rights other than those specified in 5 CFR 1201.3(a) which limits appeals of probationary employees to incidents and states that "Appealable issues are limited to a determination that the termination was motivated by partisan political reasons or marital status, and/or if the termination was based on a pre-appointment reason, whether the agency failed to take required procedures." If you cannot present evidence of one of those reasons, then legally a probationary employee is treated just like any other at will employee. An at will employee may be terminated for no reason at all or for any reason at all not based solely on the age/race/sex/disability/national origin and the employee has no recourse other than filing for unemployment benefits.
So you need to have evidence of one of the grounds in 5 CFR 1201.3(a) in order to have a viable appeal to the merit board.