Some good answers here. Two minutes may be enough time in the developer, but it seem short for fiber paper. Then, 30 sec in just water and into the fix is, IMHO, not enough. I think you're carrying a lot of developer into the fixer, thus shortening it's life.
I always develop fully, then use an acid stop. I see no problem with this as there may be with film. For fiber papers I would leave a minute. Then fix per manufacturers directions. Ilford recommends one to three minutes depending on the fixer. Then an hour wash, or less with a hypo eliminator.

In all I'd say, use an acid stop bath and mix some fresh fixer. Then, test your fixer every so often. I use a hypo check product that seems to work well.