Do not use 5VDC, but use 12VDC. This would quickly identify if the drop out is causing the problem. This still would not explain the resets when touching a ground, unless somehow the voltage drops because of touching the ground pin due to lack of protection (doubtful). I would be more afraid that the OP mentioned OPTO coupling which would inherently imply that he has two power supplies that provide separate grounds. If the OP only has one power supply, the opto circuitry doesnt work properly without the grounds being connected which means that the opto circuitry isnt even isolating.

modification:
After re-reading the original post, even touching the +5v causes this occurrence. The regulator might very well be blamed.