What is your hardware. My first reaction is this doesn’t make sense as pterm uses almost 0 CPU. Some other program may be running out of resources though, say memory.
1+1=2? 3 or more pterm sessions on a dial up? What are we talking about? Is the phditto between two nodes connected via dial up? If so, I would expect very slow response, especially if the pterms are actively displaying anything. I wonder how many bytes are in the display event that occurs when a pterm scrolls up a line? There are some strangely un-optomized things under Photon. For example, no matter how well accelerated a video card I use, If I scroll the help viewer by grabbing a scroll bar, with the help viewer window big, it is not very nice.