It depends on several factors, but the short answer is most likely weeks or more between re-supply/dump trips.
Our Outpost 35 model has very large freshwater tanks that provide drinking water plus water to wash dishes and clothes, plus take showers with. It also has very large grey and black water tanks which depending on your water usage and bathroom habits, will support lengthy off-grid stays.
Your energy usage plus how sunny it is where you are camping (which will determine how much the solar panels charge the battery bank) and how long you stay at a campsite versus drive between campsites (the battery bank is charged when you drive via the alternator-based generator system) will determine how long you’ll have battery power to run things like lights, appliances, etc. If the battery bank gets low, the camper’s alternator-based generator will turn on to charge the batteries. This combined with the large capacity diesel tanks should provide the supplemental power needed to stay a month or more if you have cloudy days and aren’t moving around much.