Chain Slips off Front Gearset
First verify these assumptions:  The chain rings are not bent (causing unintentional shifting), the chain ring teeth are not badly worn or the chain itself is not worn and stretched (causing the chain to jump teeth and perhaps feel like shifting), the bottom bracket is correctly adjusted and not wobbling (causing contact with the cage and unintentional shifting), and the leading edge of the large, inner Front Derailleur (FD) arm is not bent away from the bike (forcing a shift completely off the large chain ring).  

How your FD works: As the FD cage moves in and out, one or the other of two arms of the FD cage puts sideways pressure that shifts (de-rails) the traveling chain from chain ring to chain ring.  The FD should be securely attached in the correct position on the Seat Tube so that at no point in its travel does either cage arm contact any part of a chain ring and at no gear combination does the chain itself drag on the rear spacer that holds the two FD arms together to form the cage.  The arms should be smooth (not worn), parallel with each other, and parallel with the chain rings (and therefore in line with the chain that is traveling through the cage.) The FD spring typically forces the cage towards the IN position.  Pulling on the FD shifter cable forces the cage towards the OUT position. The inner cage arm is typically wider and longer than the outer cage arm because it requires more pressure over that larger surface area to lift the chain up to a higher gear than it needs to simply drop the chain down to a lower gear. The two adjusting screws are used to limit how far in each direction (IN or OUT) the cage can move.

Now let’s do a complete FD adjustment with the bike suspended in your work stand:  While hand pedaling the chain through the FD cage, carefully shift and center the FD cage over the small inner chain ring.  Shift the Rear Derailleur (RD) into the largest freewheel sprocket (closest to the wheel).  At this point, there should be only very slight tension (and no looseness) on the FD shifter cable.  Loosen the cable clamp at the FD and adjust the inner limit screw until the cage is exactly centered above the small inner chain ring.  Remove any slack in the FD cable at the FD cable clamp and tighten in place.  Shift the RD into the smallest freewheel sprocket (furthest from the wheel).  With the chain moving through the FD cage, shift and center the FD cage over the large outer chain ring, and verify the chain is not touching either cage arm and the cage is clearing the large outer chain ring.  Now tighten the outer limit screw.  Test all possible shifting combinations several times while hand pedaling on your work stand―first slowly then faster and faster.