It usually takes time. Sometimes hours. There are some tricks at avoiding villagers from asking favors. Here are some tips:
- Don't have any items that villagers might ask to trade/buy.
- Have your timer only, or any other tools, and fill the rest of your pockets with flowers. This will avoid villagers from giving you stuff.
- If you aren't getting any pings, talk to a villager. Every hour, they will be like "you should take a break". This stops anyone from pinging you until they give you that message.
- Villagers can only request 1 PWP a day. I also don't think they can request on days that have events or holidays, so make sure it's a normal day just in case.
- A big help to keep track of where villagers are is trapping them. This avoids them from walking all over town. I usually dig 4 holes around them on all sides to trap them. It takes a minute to do, but just keep pushing them in the section and be fast.
- Remember the villagers that are out and about. There can be up to 5 villagers outside at a time, so if you only see two or three for example, chances are you just can't find the rest (depending on the time of day). Using the megaphone helps a lot for this. It also helps if you don't do the previous tip method.
They should be requesting as long as you have your mayor permit and follow these tips. Like I said it does take a long time. It's taken me like 2 or 3 hours at a time sometimes. Just leave your 3DS on the side and keep glancing at it to look at the timer.