While one might have some sympathy for the OP, relying on a 1-hour connection was inevitably going to lead to such possibilities. Even if this is a legal connection (and I can't see how it could be even at SIN given the distances one might have to cover, and the requirement to clear security at the gate where flights lock-out passengers at 20-minutes prior to departure) it was a stupid booking to rely on. However, UA should not have abandoned arriving transfer passengers without providing an agent for its incoming flight and pre-booked some protection and had the new boarding passes ready. It is not up to SQ to wait for a connecting passenger who is not arriving on one of its flights and traveling in economy.
Also agree this should be moved to either the UA or SQ fora.