Paphiopedilum is a diverse genus, so it is hard to generalize about how long flowers last - a few days to a few months. Yours appears to be Paph bellatulum or one of its many hybrid descendants. Very short weak stems are common among these. The flowers should generally last for a few weeks to a couple months. It looks like yours had some kind of mechanical damage that detracts from its appearance and may shorten its life, but it still could last a few weeks. Conditions that are too wet or too dry can shorten flower life too.