Nan,

An understanding of the situation that you describe requires pharmocokinetic (what happens over time to the drug in the body) and pharmocodynamic (what, over time, the drug does to the body) data.

For rotigotine, Neupro, Bunten and Happe state, [1], Table 1:
t max = 16 hours
t 0.5 = 6.82 hours

The exact details vary from person to person, but I would expect a history like this:

Day 1 (Thursday, in your case). You take a dose as normal. As I understand the pharmocokinetic data, the maximum benefit from your original dose came 16 hours after it was applied. There are two conflicing processes: new rotigotine is being absorbed through the skin; half of existing rotigotine in the body is eliminated approximately every 7 hours. The paper doesn't say how long the patch continues to release rotigotine.

Day 2. You miss a dose, but you are still picking up the advantages of the previous day's dose and, possibly, any rotigotine still being released by the original patch. To start with you are probably feeling good, you have many of the benefits, but fewer side effects. Eventually, the patch runs out and rotigotine levels halve every 7 hours.

Day 3. Levels are now at their lowest. You put on a new patch and over the next 16 hours things progressively improve.

Day 4. There's a little catching up to do, but things are almost normal.

It would be interesting to know whether the patches are completely exhausted of rotigotine after 24 hours. Does the release stop because the rotigotine is exhausted or because the patch dries up, thus removing the pathway to the skin? It could be that people are throwing out unused rotigotine.

Reference:

[1] Neuropsychiatr Dis Treat. Dec 2006; 2(4): 421–426.
PMCID: PMC2671947
"Rotigotine transdermal system: a short review"
Sabine Bunten and Svenja Happe
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2671947/