Does RPM affect the length of music you can fit on a dubplate?

Yes it does. 33rpm allows for the longest recording times, followed by 45rpm and 78rpm.

How does this work?

The reason its possible to record for longer at 33rpm is that the slower the disc rotates, the longer each revolution takes. For example, if a disc is rotating at 33rpm, each revolution takes exactly 1.8 seconds. So if there are say 500 grooves, the recording would be 15 minutes long. If the disc is turning at 45rpm, each revolution takes 1 and a 3rd seconds, and so the same 500 grooves would hold just over 11 minutes of audio.

And there's more...

The loudness of the recording can limit the number of grooves that can be cut onto a disc. If the recording is very loud, the grooves must be spaced further apart, and so less grooves will fit on a disc. Generally speaking, 45 singles are cut louder than 33rpm LPs, so this is another reason why 33rpm discs tend to hold more audio.