Two thoughts spring to mind,from other threads that have cropped up from
time to time.Is the NUT slot wide enough for the wider G string? If it is binding
in there as you tune,it can shift while playing,as your fingering alters the tension
on the string.A touch of pencil lead (graphite) rubbed in there usually cures that
problem! Use the 'lead' from a propelling pencil if you have one,and move it back
and forth in the slot. The other chance,is that maybe you have a bad or rogue
string? Try a different string if you have a spare! I always use plain (non-wound)
C strings from a set of Aquilas (I use aquila strings anyway so it matches!).
But then,I use the re-entrant (high G) set,as low G anyway!
To do this I just remove the (high) G string,shift the C into the G position and
tune it LOW G,shift the E into the C position and tune it to regular C,then fit the
High G I took off,in the E string position and tune it to E. Iz used this method and
I like it.Others find the strings 'too slack' or lose volume.I don't have either problem!