How did President George H.W. Bush lose his re-election campaign? He won huge military victories against Panama (1989-90) and Iraq (1991).

Let's try this again. I've expanded on an answer I gave previously, so hopefully it's in keeping with the sub's rules:

According to a New York Times article by R.W. Apple Jr. published the day after the election:

"In the end, the exit polls showed Tuesday night, it was the faltering economy, which had bedeviled him all year, that finally did in George Bush.

"From the New Hampshire primary in February, through the party conventions this summer, to the unofficial start of the general-election campaign on Labor Day, public opinion held remarkably steady: three-quarters of the American people, according to New York Times/CBS News polls, disapproved of the way Bush was handling the economy."

CNN exit polls found similar results. American journalist Robin Toner wrote in the November 5, 1992, edition of Australia's The Age:

"...[T]he [CNN] exit polls showed economic discontent and a hunger for change were two of the engines of the Democratic victory.

"The exit polls showed that seven in 10 voters considered the economy poor or 'not so good', and Clinton ran strongly among them.

"Mr. Clinton survived with a remarkably disciplined campaign that stayed focused on the economy and what he often called 'the forgotten middle class.'

"Jobs and the economy were cited by nearly four in 10 voters as the issue that mattered most in ther decision. Health care and the deficit, an issue pounded by the Perot ticket, were the second-most important issues, each cited by about a quarter of the voters."

Though by Election Day, Clinton's win was predicted, his performance nonetheless came as a surprise. Of this, Toner wrote:

"[Clinton's] campaign represented the culmination of years of effort by centrist Democrats to redefine their party and reconnect with the middle class.

"It also represented an extraordinary turnaround for a party that for much of 1991 seemed destined to lose to a president soaring in the approval ratings in the aftermath of the Gulf War."

One of Clinton's campaign slogans in 1992 was "It's the economy, stupid." Conversely, one of Bush's biggest gaffes during the campaign was when he accidentally called a reception a "recession". The economic recession was an issue that Bush was not able to escape throughout the campaign.

In fact, scholarly articles analyzing the election have focused on the major campaign issues being the economy, which hurt Bush, and "candidate character", which Bush tried to use against Clinton, but was ultimately unsuccessful.

Ross Perot played something of a role, but as it turns out, most analyses found that his effect on the outcome was probably negligible. The New York Times exit polls found that he actually hurt Clinton slightly more than he hurt Bush, so the third party wasn't directly Bush's undoing. Again, according to R.W. Apple Jr:

"After months of speculation about whether Perot backers came principally from the Bush camp or the Clinton camp, the exit polls provided an answer of sorts: They came from both sides, with slightly more people saying they would have voted for the Democrat if Perot had not made his late reentry."

The L.A. Times exit polls had similar findings, as published in their November 5, 1992, edition.

That said, weak incumbents or incumbent parties often face a third party challenge--it happened to Carter, it happened to Hubert Humphrey, it happened Truman, and it happened to Taft. All but Truman lost, and Truman won with less than 50% of the vote in the election that famously produced the "Dewey Defeats Truman" headline. (He actually went on to run again in 1952 but was so weak at that point that he lost the New Hampshire primary and then dropped out.)

In other words, third parties aren't often the cause of an incumbent loss but are an effect of a weak incumbent who is on his way to losing. To that point, George Bush in 1992 remains the only Republican incumbent president to face a serious primary challenge since the New Hampshire primary was first held back in 1916. Pat Buchanan ran against Bush and finished with over 35% in New Hampshire, and won 20% or more of the vote in every state but one through Super Tuesday on March 10.

In the early months of the campaign, Bush did try to run on his war record, but according to historian David Halberstam in his book War in a Time of Peace: Bush, Clinton, and the Generals, Americans weren't interested anymore. With the Cold War over, they began looking inward, more free of foreign threats than the United States had been since before World War II.

Thus, ultimately, the Gulf War of 1991 did little to help George Bush in the 1992 election. His domestic accomplishments were modest and, as the exit polls bore out, several domestic issues were most important in deciding who to vote for, while foreign policy was much lower down the list. This hurt Bush and helped Clinton, and Bush lost because of it.

TL;DR: It really was the economy, and more broadly, domestic issues, that did Bush in, whose major accomplishments were almost entirely on the international, not domestic, stage.