Both the particle tracer and the particle pathlines filters are special in that they capture and modify geometry as they iterate over time. Thus, the save state, which just captures the state at a particular time, cannot capture this geometry or properly restore it.
For the particle tracer, you will also have to save the data of the particles the filter is generating and then load them back in as your seed points. There is no automated way of doing this; you would have to write your own script or do it by hand. For the particle pathlines, I can think of no way to do it other than to rewind time to the beginning of the path segment and run back through (or to change the filter itself to accept initial geometry).