Does that mean they get to do all this again?
Lets wait til the Republicans do their cross. No, they have no control over what Democrats do next but this narrative isnt baked into the cake yet.
If so, it would fit into my theory of pushing this out to next October.
There must be some procedure available for the House to impeach the President and then never actually refer those charges to the Senate.There is, but the timing does not favor the Democrat strategy.
The procedure would be to vote to impeach in the late stages of the Congressional session (say, October 2020 before the election), hoping that the October Surprise is enough to keep Trump from winning. Then the Democrats would delay the Senate (which would likely go into recess until after Thanksgiving) until it adjourns sine die at the end of the year, claiming a lame duck Senate shouldn't hold a trial on a President who just faced the voters.
By adjourning sine die, all business before the Senate would be deemed completed, and the articles of impeachment will expire with all other pending legislation. If Trump wins reelection in November 2020, the next House would have to start all over in January 2021.
-PJ