As the impeachment process plays out, the 2020 presidential election grows ever closer. Up until recently even many of Trump’s detractors asserted that because the election is so close, Trump should not be impeached. The infamous Ukraine call changed the view of some on this matter, but Trump’s defenders still use this argument. Some also argue that impeachment would overturn the 2016 election and thus should not be done. There are thus matters to be considered—whether impeachment should not occur when an election is close and whether impeachment wrongly overturns an election.

As Trump’s defenders rightly note, Trump was elected president. As his detractors note, he lost the popular vote by a large margin. The impeachment process could result in Trump being removed from office and one could claim that this would overturn the election. But this would be an error.
First there is the obvious point that impeachment is in the constitution and thus is intended to be an option—if the founders saw it as a wrongful overturning of elections, they would have presumably not included it. While the Republicans praise the wisdom of the founders when it matches their agenda of the moment, the founds were but men and could be wrong.
Second, the purpose of impeachment is to remove a person from office who has committed misdeeds that warrant removal. This is not to say that impeachment cannot be abused, but to reject impeachment because someone might abuse it would be analogous to rejecting criminal courts because they might be abused by some judge. It is not the process but the abuse of the process that would be a problem. If this Republican defense worked, then they would have just proven that they were wrong to impeach Bill Clinton and have shown that no one (even a Democrat) should ever be impeached in the future. I suspect that those advancing this defense of Trump would not apply it to Clinton or a future Democrat but I could be wrong about that—perhaps they have a strong and abiding commitment to the principle that impeachment is always wrong because the person being impeached was elected.
Third, an analogy can be used to show that this defense is flawed. If the principle is that when a decision is made by people to select someone for a position, that person should never be removed until the time comes to again select for that position, then no one should ever be fired, and no one should ever be divorced. This is clearly absurd. Now, what about the upcoming election defense?
It could be argued that with an election coming up, the people should get to decide whether the president remains in office or not. One challenge here is sorting out a time limit for this. Trump has over a year left in his term, so if the defense holds now, then a president would be immune to impeachment for about 25% of their term. This seems odd. If the president is justly impeachable, allowing them a year (or even a month) to continue to engage in misdeeds seems wrong and harmful.
Consider the following analogy. Suppose that Hillary is hired by the board to be the CEO of a corporation. In her contract, she will be up for review in four years. Hillary engages in misdeeds, including efforts to corrupt the review process. Imagine that the corporation has a policy that allows such CEOs to be removed for bad behavior, but Hillary insists that terminating her before then would overturn the vote of the board, so she should be allowed to stay and to continue her subversion of the voting process and commit even more misdeeds. This is absurd and would merely allow her more time to commit crimes and work on unjustly keeping her position. The same holds true for Trump.
As another example, imagine a professor who is using their position to extort favors from students. They are caught, but the university says that since they are up for tenure review in a year, they should not be fired—this matter will be sorted out by the vote of the tenure committee. This is also absurd—even if the vote is coming up the next day, these misdeeds should be addressed. The same applies to Trump.
Thus, the election defense of Trump has no merit. This also holds true for any other president—even a Democrat.