Can the repeated and unexplained disappearance of money from a wallet, even after ensuring it has been counted and not left unattended, be due to a satanic act?

There is no definitive explanation for what is happening to you, but it is likely the work of Satan. It is established in the Sunnah (definition) that Satan does not open a closed door, untie a knot, or uncover a vessel if the name of Allah has been mentioned over them. It has been narrated from the Prophet, peace and blessings be upon him: "Close the doors, tie up the water-skins, overturn the vessels, and extinguish the lamps, for Satan does not open a closed door, untie a knot, nor uncover a vessel." Some scholars have qualified this by mentioning the Basmalah (saying "Bismillah"), meaning by mentioning the name of Allah. If the name of Allah is not mentioned, then it is possible for Satan to do so.