My heart almost stopped several times while under anesthesia - what sorts of things can cause this?

If you could: Be more specific, saying your heart almost stopped doesn't mean anything to me.

Could be?: Your heart "almost stopping" could refer to few things. Heart rate getting very slow, arrhythmia causing ineffective and/or slow normal beats. Some congenital conditions may predispose you to arrhythmia and conduction disorders. Surgical stimulus may cause slowed heart rate due to vagus nerve stimulation depending on location of surgery. So depends on what exactly is meant

Discuss: i would discuss this with the surgeon and the anesthesiologist ; very rare event under GA in a 30 y/o

Rarely occurs: There are multiple causes, including overdose of anaesthetic medications, low blood pressure, and inadequate delivery of oxygen, just to name a few. General anesthesia, like any other medical procedure is not without risk.