The NaOH followed by the heat is what causes decarboxylation. The oxalic acid is added to give you a stable amine salt that easy to isolate from the crude mixture. If you want to check my explanation, take NMR of the filtrate that is collected after the first step before the material is resuspended and oxalic acid is added.
I think you didn't understand my last explanation of the mechanism. I freely admit I am guessing here, but I don't see how stirring in room temp oxalic acid causes decarboxylation, and if it did why you would need to cook the molecule in hot NaOH beforehand.
Here is what I think happens in that prep:
The NaOH deprotonates the thiophenecarboxylic acid to give the carboxylate sodium salt, which will thermally degrade to CO2+aminothiophene anion. Thiophene anion gets a proton from water. HCl is added to precipitate the impure aminothiophene HCl salt. Impurity is probably starting material and whatever aminothiophene degrades into, which is also an HCl salt now. The crude aminothiophene HCl salt is dissolved in acetone, then oxalic acid is added. The 2-aminothiophene oxalate salt is not soluble in ether, while the methyl-3-amino-2-thiophene carboxylate oxalate salt and whatever other garbage is around is soluble. Collect the pure starting product by filtration.
As for refluxing for more than 30 min, I think you need to be careful. Aminothiophene is apparently not that stable. It is possible that longer reflux will degrade it. You may just be losing yield during your workup steps just during glassware transfer and such. That NMR of the crude I suggested should show conversion, which will give you the yield you're "supposed" to get.