Besides the (continuing) funding aspect that was covered in the accepted answer, some additional ones that have been raised in the press:
Trump's ego/image. Does not want to be seen as having "gone down" without having exhausted every angle. Remember all the nicknames he put on competitors from "low energy" to "losers" etc.
in tandem with just getting more funds, it keeps the Republican base energized and still focused on Trump. E.g. (referring to Nov 11 survey):
A recent Economist/YouGov survey found that 8 in 10 Trump voters said Biden’s election victory was not legitimate despite all the evidence showing that it was.
That number seems to have come down a bit in a more recent Ipsos-Reuters survey and a Rassmusen one, but still a majority of Republicans think the election was somehow illegitimately won by Biden.
Such high numbers could potentially have offered political cover for Republicans in canvassing boards and even state legislatures to push the (state) constituional/legislative boundaries like not certify elections results, which might have given Congress a say in the outcome, be it by not accepting some states' results as "irregular" (e.g. if given past a certain deadline), and/or ultimately--as was suggested in another answer--a downright contingent election.
Trump relished the prospect of a contingent election, because the House of Representatives' votes in such an election are weighted differently than for regular votes. Lawyers that were associated with Trump have also been fairly explicit about this:
Harvard Law professor emeritus and Trump impeachment defense attorney Alan Dershowitz explained why postponing certification is such an important part of Trump's attempt to have the election decided by state legislatures or the U.S. Congress. [...]
"The goal here is to try to just make sure that by the date the electors meet and vote there aren't 270 votes for Biden." [...] "If they can bring down the number of electors... from the 305 and bring it down to 267 or 268 then the election goes to the House, where the Republicans win," Dershowitz said.
Likewise (the short-lived Giuliani sidekick) Sidney Powell said their goal was to:
"invalidate the results of the election and force it to the legislatures and the Electoral College and the Congress if necessary."
Explainer of how a contingent vote would favor Trump:
When the House determine an election outcome, it's not by a majority of votes by individual members. Rather, each state votes as a delegation. Republicans hold a majority of states by delegation, even though Democrats have a majority of seats. In the 116th Congress, Republicans control 26 states, Democrats control 22 and Pennsylvania and Michigan are split. If the vote was down party lines, Trump would win.
Although ostensibly done for other reasons (than applying pressure on them), Trump for example had phone calls with the Republican Wayne county commissioners who announced they were rescinding their certification votes. Likewise he met with the Republican leadership of the state's legislature soon thereafter. The RNC sent a letter to Michigan's Republican state board member urging them to delay certification by conducting another audit. (One of the Republicans on this state board abstained, but the other one did not, so the results were certified.)
On Dec 3, Giuliani publicly pleaded his case with Georgia's Senate (committees):
Former New York City Mayor Rudy Giuliani was in Georgia on Thursday to make claims of widespread voter fraud at one of two [Georgia] Senate committee hearings held on election security. [...]
Giuliani urged legislators in the Senate Judiciary Subcommittee not to certify the election results and said that Georgia’s senators could use their constitutional power to appoint Georgia’s electors.
“You are the final arbiter of who the electors should be and whether the process is fair or not,” Giuliani said. “The other way to look at it is, it’s your responsibility if a false and fraudulent count is submitted to the United States government. And it’s clear the count you have right now is false.”
All this immediate benefit aside, there are potentially long-term benefits to Trump's faction in the Republican party to propagate the legend that Trump's loss was illegitimate. Some commentators have drawn an analogy with birtherism (the belief that Obama was not born in the USA, thus not a legitimately elected president), which stayed at relatively high numbers throughout Obama's presidency (and possibly still stays that way, although it doesn't get polled much recently) as a motivator for a good part of the Republican base.
Feelings that a historic injustice was perpetrated against one's side/group have fueled some political movements (fairly) long-term in numerous cases before. It remains to be seen if Trump's election loss turns out to be one of those.