Campaign Operations, Corrected Third Printing
How exactly are the Availability Rolls described on page 13 supposed to work?
By the rules as written in the last paragraph on the page, you get one Availability Roll per combination of chassis, variant, and crew experience level. This limit appears to apply regardless of success or failure. Failure obviously means you cannot acquire that combination, although you can try again after changing at least one of the three variables. Success means you can acquire at least one of that combination, although it is not stated if that is limited to exactly one instance, or if it is possible to acquire more than one instance after the single successful Availability Roll.
However, when moving to the examples, the rules they are operating under seem to be different. The example of "Hannah" on page 15 explicitly has her making an Availability Roll multiple times (four times, in fact) for a Veteran Warlord (BLR-2D) - the exact same combination of chassis, variant, and crew experience level each time. It is very possible that this was intended to be allowed, in which case the rules on page 13 likely need to be adjusted for clarity. Alternately, the rules on page 13 are correct and the examples need to be adjusted. To determine which, we need a ruling on what the developer intent was here.
For context, I should note that the Mercenary's Handbook (FASA 1616, page 34, second column, first paragraph) had unit acquisition done in such a way that a warrior or crew was selected, and then availability rolled for a unit, with only one chance to acquire any specific unit - but with an explicit note that the "one chance" only applied for that specific warrior or crew, and the next warrior over had their own independent chance to acquire the same unit. This biases me towards thinking the examples are correct and the rules should be adjusted.