I am looking to offset print a poster and can't find a service that does above 36"x48". Is this the largest size offset printing can accommodate? What's the cause of this limitation?
The big size of the machines?
The low demand for bigger sizes?
The maximum paper size?
Actually depending on the country you live there is a chance you can not find a suitable paper, for example more than 72x102cm.
But for example some Heilderberg machines can print up to 121x162 cm https://www.heidelberg.com/global/en/products/press/sheetfed_offset/speedmaster_xl_145___xl162/technical_data___equipment_11/technical_data___equipment_22.jsp
In case you find a printer that big, you need to see the minimum ammount of units they are willing to print.
The bigger the machine, the bigger the number of thousands you need to print, because it cost a lot to have them paused mounting the new plates.
I discovered about a dozen offset printers doing 64" and 81" in the United States. The secret was to search for the specific machines that can print at these sizes, like the KBA 164 (64"), KBA 145 (57"), KBA 185 (73"), and KBA 205 (81").
Printing companies more often advertise their acquisition of one of these expensive machines than their maximum sheetfed offset capability. You'll also find press releases mentioning the machines that'll lead you back to the companies.