I have a year lease on an apartment in Los Angeles that will expire in August. The landlord wants to convert it to month to month. Can I require another year lease?

Yes, the landlord can change to month to month, and no, you can't require a year lease... I am 99% sure anyway.
The LA code is complicated.
I suspect that your landlord wants to be able to sell the building or condo you are in (a guess based on rising real estate values).
What he can't do is terminate your tenancy very quickly, as long as you are a good tenant.

This is the best I could find:
American Legal Publishing - Online Library
Scroll down to 151.22 - Ellis Act. It covers many situations.
There is also federal legislation that protects tenants if a seller is foreclosed on. There is a post at the top of the Real Estate board about it.