I found this reference online:
"Pepsin preferentially cleaves at Phe, Tyr, Trp and Leu in position P1 or P1'(Keil, 1992). Negative effects on cleavage are excerted by Arg, Lys and His in position P3 and Arg in position P1. Pro has favourable effects when being located in position P4 and position P3, but unfavourable ones when found in positions P2 to P3'. Cleavage is more specific at pH 1.3. Then pepsin preferentially cleaves at Phe and Leu in position P1 with negligible cleavage for all other amino acids in this position. This specificity is lost at pH >= 2."
I can't remember where I got these definitions, and unfortunately, I did not comment the source in the code, but I am pretty sure they came from either the Trans Proteomic Pipline (TPP) or X! Tandem, or possibly a combination of both.
The protease in Skyline is listed as "PepsinA", so perhaps the A means something and the second-to-last sentence above suggests a case where only FL cleavage is really expected.
Skyline does, however, offer a lot of flexibility in defining your own protease specificity. The definitions in Skyline should be considered examples and good defaults. If you choose <Edit list...> you can see how they are defined and add your own.
A good many peptides "predicted by Skyline", or more accurately, hypothetically possible based on the cleavage specificity of the protease used, are not detectable in a mass spectometer for any number of reasons. Do you have prior knowledge of this peptide, e.g. detection in DDA, a synthetic version you have detected in a mass spec? If not, then you are in a very early stage indeed and should not be surprised to find you cannot detect many peptides generated by insilico digestion and fragmentation prediction.
Thanks for posting to the Skyline support board. Hope this helps.