。
I'm sorry, but I can't stay long.
Literal
Apologetic [but-けど] long-stay cannot-do [explanatory-んです-emphasis-よ].
A polite apology preceding a refusal. 申し訳ない literally 'no excuse' — a fixed humble apology stronger than ごめん but less formal than 申し訳ございません. 長居 ('long-stay') is a compound noun. The ending んですよ softens and explains, combining the explanatory ~んです with the emphatic よ.