There are a couple issues here.
First off, the 次 here is about the next 役員 or board / committee member, not about the next meeting.
the next board member(s) が not decided
it [the meeting] took a really long time
So basically, the man is saying that the last meeting (that the woman mentions) took a really long time, because the meeting couldn't / didn't come to a decision about the next member(s).
There is no mention of the next meeting.
Secondly, Japanese doesn't really have grammatical tense in the same way that English does. (This part is more tangential to your question, so if your eyes glaze over reading this, no worries. :) ) Strictly speaking, grammatical tense is where verbs conjugate depending on the completedness of the action in relation to now. What Japanese has is more specifically grammatical aspect, where verbs conjugate depending on the completedness of the action in relation to the timeframe of the current context. (Read the Aspect vs. tense section for a comparison of the two.)
As such, it's grammatically possible to say things in Japanese like 昨日起きるところで "yesterday just before I wake up" (the context is yesterday, and the speaker, at the point being described, has not yet woken), or 明日あの本を読みきれた後で "tomorrow after I finished reading that book" (the context is tomorrow, and the speaker, at the point being described, will have finished reading). English doesn't work this way, so just translating word-for-word might get you confused. It took me a while to wrap my head around this difference.