、、、。
To be continued next time — so, please, I humbly ask for your continued patronage.
Literal
Next-time [to-に] continue, [quotative-と]-[thing-いう]-[with-で], please continued-acquaintance [extent-のほど], earnestly please.
Closing remarks register, typical of serialized blog posts, manga tankoubon afterwords, or newsletters. 次回につづく is a fixed serial-ending phrase ('to be continued next time'). ~ということで is a discourse connector that frames the preceding as established ('so, with that being the case'). お付き合いのほど is an elaborate formal collocation for '(your) continued acquaintance/patronage.' 平に is an old-fashioned adverb 'earnestly, flatly' (as in prostrate/humble), intensifying the request. お願いいたします uses the humble (kenjōgo) form いたします for maximum formality.