Can my US passport be denied if I lost it more than three times?

You can't be denied a passport simply because you're forgetful, but you might be denied expedited processing. Somewhere, an officer is wondering what happened to all those passports you lost, and whether they might have been stolen or misused.

The reasons why one might be denied a US passport include:

• Submitting low quality passport photos
• Failing to fill out the application completely
• Failing to include payment
• Failing to include legible and valid supporting documents
• Not being a US citizen
• Owing more than $2500 in child support payments
• Owing back federal income taxes, in some cases
• Having pending felony criminal charges
• Being on probation or parole for a felony

If you had such a circumstance apply to you and your circumstances recently changed, it might not be possible to get expedited processing as the change in circumstances will need to be verified.

Further, if you have a history of lost/stolen passports, and you lose a passport while overseas, the embassy or consulate may issue a limited validity emergency passport which is only good for one year, rather than a full 10-year validity passport.

While I know we dislike link only answers but do we really want to reproduce the relevant, lengthy sections of the US Code of Federal Regulations here? If not, then 22 CFR 51.60 - Denial and restriction of passports is the answer. (The main reason I wrote this one is because Michael Hampton's otherwise excellent answer links to the USA Today which I find slightly less trustworthy than the CFR itself.)

What is notably missing from Michael Hampton's list for someone who tends to lose their passport:

The applicant is in default on a loan received from the United States under 22 U.S.C. 2671(b)(2)(B) for the repatriation of the applicant and, where applicable, the applicant's spouse, minor child(ren), and/or other immediate family members, from a foreign country (see 22 U.S.C. 2671(d)); or

So if the embassy loaned you money to get you home because you were destitute then you can't get another passport until you paid back the loan.

Also, if your forgetfulness reaches really badly serious levels and

The applicant has been legally declared incompetent by a court of competent jurisdiction in the United States

then you also won't get a passport.