I think the studies below gives a lot of insight into the acid-stability of the methylenedioxy ring (and piperonal in particular, of course), at least when it comes to moderately strong acid solutions - It's well known that someting as strong as sulfuric acid damages the molecule significantly.
Stability of Piperonal toward Boiling Formic Acid (95%)
Piperonal (2.000 g,) was refluxed with 95% formic acid (20 cc.) for sixteen hours following the method of Wright and Hibbert.[14] After removing the formic acid under reduced pressure, the residue was dissolved in ether and the ether solution extracted with cold 1% sodium hydroxide solution. The ether extract was dried over anhydrous calcium chloride, concentrated, and the residue distilled under reduced pressure. The distillate (1.696g., equivalent to 84.8%) crystallized at room temperature, mp 36-38°C. A mixed melting point with the original product showed no depression.
Stability of Piperonal to Hot Ethanol Containing 3% Hydrogen Chloride
Piperonal (2.000 g) was refluxed for twenty-four hours with absolute ethanol containing 3% hydrogen chloride. These conditions were somewhat more drastic than those used for the ethanolysis of maple and sassafras woods. The ethanol was removed under reduced pressure, the residue dissolved in ether, and the piperonal isolated as above: weight of recovered piperonal, 1.827 g (91.3%).
Reference: J. Am. Chem. Soc. 61, 2198 (1939)
