I say yes to everything even if I know I'm not going to be able to catch a specific bug or fish (not sure whether not doing a request or denying a request lowers friendship more??) but I try and do everything else right away or else I'm certain I would forget. Sometimes I jot down what everyone is looking for if I get several in a row and I'm in the middle of doing something else. If I agree to meet someone at their house or my house at a later time, I usually set a reminder on my phone, because those I definitely forget.
I've read several times - I think the original source was a Japanese forum? Well whatever, apparently taking on a request and then not being able to complete, lowers friendship (one level) while refusing a request is neutral.
Some circumstantial evidence this is correct, (poster: stitchmaker). Sometimes I comply with this idea but often I just accept and hope to fulfil. A letter with a gift attached makes up for any lowering of friendship level.
I avoid visits which are 30+ mins in advance: either by accepting and then pressing quit - which makes the villager shrug, but apparently this will lower friendship; or refusing outright, which I think gets a more sad response from the villager. Whatever, just send a letter with a gift attached to balance it out.
I found tasks in acww better programmed, I think you had 3 days to complete and if not fulfilled then the villager said they no longer needed the item. (excepting deliveries to other villagers which were to be done within the hour?).
Now in acnl, we get till the end of the day for all requests, which is very tight for some fish/bug ones. Nor do the villagers ever say anything about no longer needing the item, its just left hanging.
However getting the gift for completion, coming from the recipient is a lot better than having to run around trying to find the requester, to get the gift for completing the task. Albeit I do try and find them to say delivery made.
In all ac games the quantum leaps villagers can make is just the same. They can disappear fast.