Why does my guitar pre-amp lose it's offset?
The MCP6001-1R-1U-2-4 datasheet specifies a few key points:

Section 1.0 Electrical Characteristics: Input bias current is 1pA, so the opamp is essentially a JFET-input class.  Maximum output voltage swing is within 25mV of power rails, so device is also rail-to-rail output, despite it not highlighting either on the front page.
Section 4.3 Capacitive Loads: If C4 is really 10µF (and whatever after it is a fairly low impedance), a resistor in front of C4 may help. Temporarily replace the electrolytic caps with solid ceramic ones (surface mount, value not critical) - just to see if they make a difference.
Section 4.4 Bypass capacitors: do you have these installed?
Section 4.5 Unused Opamps: has this been followed?
Section 4.6 PCB surface leakage: is the board design causing leakage? Layout is important for the input. Even residual flux can cause leakage at this high impedance.

Edit: since adding the resistance before C4 helped, the issue must be that whatever is after this stage is too low of an impedance for this opamp. A solution may be to use the other amp in this package as a &quot;unity-gain follower:&quot;



simulate this circuit &ndash; Schematic created using CircuitLab
There is still an output capacitance limitation in the &quot;buffer&quot; stage, but the effect may be minimal as the gain is just 1:1.
Note that C1,R1,R2 form a high-pass filter on the input; 0.1µF likely would give very little low-frequency response, so it was bumped to 1µF. Some experimentation may be needed.  Added C5 per datasheet.