Have you actually got a ground pour on the board?
Or is it just a copper pour that's not connected to ground?
A floating pour may well be the issue going off your description, while it's in your hand it's being grounded via you & when on the table it's not.
Or it could be because you have 3 ground nets Earth, GND and PGND and I cannot see any connection between them in the schematic and you have some parts referenced to Earth yet other parts of the same circuitry reference to PGND etc.
Take IC2 where the 3.3v is generated from the 4v (I assume) - it references to Earth.
The flash IC is powered by 3v3 yet it's return is via PGND, as is L8, looking atthe other IC's they doo are supplied by 3.3\4v but return via PGND.
C11/C12 - I assume decoupling caps for IC4 (main processor ?) are referenced to PGND yet IC4 has a GROUND return so they will be ineffective.
So it could be you have split grounds that are not connected anywhere and when your holding the board you connect them (possibly via capacitance) and then when on the desk they are separate again.
Can you go through the whole circuit and review the grounding & return paths?
By the way, there are plenty of free PDF generators you can get that do not slap big watermarks across the output, like PDF995 - I like this one as I can edit, join, split pdf's also.