Are there any instances when you would not perform 3 consecutive daily dialysis sessions when initiating a patient on hemodialysis?  

In-patient - Friday, Saturday, and Sunday (we are not fully staffed on Sundays). Out-patient - I see no reason to do three days in a row. There is nothing magical about starting dialysis. Patients were surviving without it before you started it, there is no rush.   Updated answer: YES ...

Outside of the US, at least in Thailand, the usual practice is not to do 3 days in a roll but to actually do around 2 dialysis sessions in the first week tailoring to what metabolic parameters are needed.