I have noticed that there is some variability to the speed and the contrast of the print that I think may be attributed to the age of the developer. I noticed this when I replenished my developer recently, and it appeared to cause a change in contrast and also a slight speed change.
So, while you can let the PO go as long as you want, and simply replenish it on occasion, I think it is much better to get a set amount of PO, and then replenish it back to that level on a regular basis.
This will cause the nature of the mix to remain a bit more stable from the unreplenished developer to the freshly replenished developer.
There have been some discussions regarding the fact that the PO does become heavily loaded with both metal salts and FO, and it does have an effect on the final print, and I think that some staining and the dreaded salt migration can be partially attributed to the amount that the PO has of FO and salts.
I have recently started increasing the replenishment rate by pouring off a few hundred ml of PO at the end of a big printing session. I have done this because I think that it may help keep the highlights clean and also help eliminate any possible staining that might occur. This is not based on direct experiential data, but is simply a hunch based on some anecdotal evidence I have.