I usually save yeast from my primary when i transfer to my lager carboy and use it within a couple of days, going by the mr. malty tables for the amount to use in my next brewed lager. I do this up to 3 times then pitch new yeast. How long could i keep the harvested yeast and pitch direct without having to make a starter?
Yeast are hardy little critters. Flag porter from England uses a yeast cultured up from a bottle that sat on the bottom of the English channel for well over 100 years.
A starter or oxygenating the wort well before pitching is a good idea with refrigerated slurries. The viability doesn’t drop much at all even over a month, but the sterol content likely will.