How has the hash rate for bitcoin continued to increase despite price drops and miners dropping out?
the hash rate for bitcoin tripled from around 15 EH/s to 45 EH/s. Why is this the case?


Well, at the simplest level, that means more hashing power is being used to secure the network. 

This could mean that a larger number of ASIC units are running, and/or that more efficient ASIC units are being created and used. A more efficient ASIC would perform more hashes per second, for a lower cost per hash per second. 

Every miner will have their own costs, motivations, etc, so it’s hard to speak broadly about ‘what miners will do if price is x and the hashrate is y’. For example, a price drop means some miners with the highest costs may no longer be able to operate profitably, but perhaps those miners are ideologically driven, and will take a loss with the hope that the bitcoin they mine will one day be worth more than it is at that time. Etc.