The answer to this question depends on where you live and if you have rent control. I am in Toronto, Ontario Canada so I can explain the rules here.
First of all here the lease automatically goes month to month after the first year lease is up.
You must give 90 day notice of rent increase. The tenant has to give 60 day notice before moving out, so if they can't afford the increase, they can give proper notice.
For apartments built before November 1991 we have a prescribed rent increase amount given to us annually by the government, the maximum is 2.5% if the tenant moves out, you can raise the rent as much as you like to a new market rent, but then your annual increases are limited.
You can also make another application and go to the Landlord & Tenant Board to increase the rent 3% per year for a maximum of 3 years (9% total) for capital cost allowances.
For Apartments built after 1991... no limit, except once annually and if you raise it too much your tenant will move out. I'm currently raising rents $100 to $150 per month in some places. It's worse if I don't do it every year, the maintenance fees go up every year for the owners and the rent falls far behind. Then the owner wants to sell or get rid of the tenant or do a huge increase like $350 per month.