ichidan verb, transitive verb
drink regularly; be accustomed to drinking
Often used for habitual drinking of alcohol, but can apply to any beverage. The 'stubbornly' gloss is rare and context-dependent; the core meaning is regular or habitual drinking.
彼は毎晩ビールを飲み付けている。
He drinks beer regularly every night.
この薬は飲み付けていないと効き目
This medicine won't work well unless you take it regularly.