I'm just wondering if you were as precise in your ASSEMBLY as you were in the measuring and cutting.
A few years back I used to make a lot of A-frames for a local signwriter, a mixture of both four- and three-legged frames, either of which could have display panels on one or both sides. The choice of three or four legs was usually decided by their intended use: three-legged on rough ground, four on level floors, the inherent stability (as Big All and Woodsmith have said) of the three-legged ones also made them good for use where there was a lot of foot traffic and the board was likely to get knocked. (4-legged ones 'collapse' easily if knocked hard enough for the legs to move closer together, whilst 3-legged ones just move around a bit. Oh God, cafes all over the country are now going to be hit by a spate of collapsed A-boards as people go around trying to prove me wrong!
)
On the four-legged ones, when assembling the component parts I always "mirrored" them for assembly, checking the diagonals for squareness on both the first half AND the second half, despite fixing the second half together whilst it was lying on top of the first, aligning the two.
I'd then fix the hinges to the top of the one half then stand them on a flat surface leaning against each other AND THEN FIX THE OTHER HALF OF THE HINGES to the top of the other side.
Anything in that assembly procedure needed only to be a fraction out to add a wobble, and you've got one hell of a wobble!
Disassemble and start again.