Does starch thickened custard get thinner after a few days?
It is not the starch alone, but the combination of starch and egg yolks. Yolks contain an enzyme which digests starch after some time, making the whole custard thinner.
If you absolutely have to use a custard with both starch and yolks, either consume it quickly, or boil it well (at least of minute of visible bubbling) to deactivate the yolk enzymes.