Bob still remembers somethings and his still doing all the stuff he was mean to do the day before (however long that was ago). Eventually Bob should get curious. Why do I have so much food, why does my friend say I have sent 30 letters, why is there so much pizza boxes.
This creates a very interesting story scenario where one day Bob will realize something is a bit off in his life. He investigates it, but before he can finish, its a new day and he forgets again. So one day, Bob realises that something is going wrong and that he forgets every time he goes to sleep and he leaves himself clues. Small things like a broken up which wasn't meant to be broken. A painting with a part torn out or missing. Hidden notes around the house written cryptically and messy because he was in a rush when he wrote it.
Basically, after a long enough amount of time, Bob should realise something is wrong, try to leave himself clues or keep a diary or write notes and this continues until he figures out why. Once he figures out why, he can either try to solve it, try to save his neighbors or the story ends.
Another potential solution, would be for everyone to stop sleeping. Crazy idea isn't it. Most people can't function after a day without sleeping, but a potential solution would be via meditation or very short naps (where you are forced awake before you reach deep sleep). If you can identify what stage of sleep resets your memory, then you can force people to adjust their sleeping patterns and lifestyle to never reach that stage.
The final method, would be having every person watching a video recap of what they have been doing the last couple of days or keeping a log and reading it first thing in the morning. If bob sees a paper going, get groceries, why would he keep it after he got the groceries. Why hasn't he written down what he did. The same applies for all his schedules, tasks, meetings, catchups, chores and what not. Once a person has started, they read their note book, know what they did the day before and can do what they want/need today.
Let me introduce myself... Well, call me Bob. I know my name, my age and where I live. I work as a programmer on a software industry, and I pretty much now how to code.
But my problem is... I forgot what I did yesterday, but I wrote it all down. Yesterday was my birthday. I wrote it down and there is a picture of me. I had pizza and there are several boxes in the bin that I should throw out today. The garbage collection comes every Wednesday and today is Thursday, so its going to be another week before they are removed. Hopefully there is enough space in those bins.
I have a crossed out note on my desk about buying groceries. I have a pretty large stockpile since I kept forgetting out it. But now I just make a note and cross out what I brought and I don't need to worry. I think I'm out of milk though. I'll just make a new list and write milk on it.
I should also go buy a bald brush. I accidentally kept trimming my hair until there was none left. Good thing I burned that note. Lets me add that to the grocery list so I won't forget tomorrow and repeat today again.
I also need to write a letter to my friend on earth. I checked the postmans website and it says I sent him 30 invitations already. I'll just say its a administrative error. Better make sure to write that down on my to-do list so I don't forget either.