While I agree with everyone else that taking a month off is probably not the best solution to this asker's specific problem, I feel like it's also worth answering the actual question asked, "Can I Ask For a Month of Unpaid Leave?"
There's a term for this: Leave Without Pay, often shortened to "LWOP".
Larger companies with HR departments should either have a formal LWOP policy, or, have a policy to not have a policy. There should never be any harm in asking what your company's policy on LWOP is.
The standard definition is set out on this US Chamber of Commerce "HR Practitioners" page. While an American page, the policy is identical to the basic terminology my last British employer used, so it appears to be pretty standard:
Leave without pay (LWOP) is an approved temporary absence from duty in a nonpay status re-quested by an employee. The term does not cover a suspension, furlough, an absence for which leave has not been approved, or nonpay status during hours or days for which an employee would be compensated on an overtime basis.
Extended LWOP is a period of LWOP exceeding 30 calendar days.
The authorization of LWOP is a matter of administrative discretion and may not be demanded by an employee, except that [three military and family related US-specific exceptions]
But note that it is a case of authorisation, do you should expect to go through some kind of application process, which will likely include explaining why you want this leave.
To give one real-life example, my previous employer's LWOP policy was something like this:
- You needed your manager's approval for standard (<30 days), and approval from higher up the food chain for extended (>30 days) including a conversation with HR about whether a temporary replacement was needed
- There was a formula for how much notice needed to be given. I believe it was roughly double the amount of days requested, although exceptions could be made if the need was an unexpected emergency
- For extended LWOP there was an expectation that you give a business justification (which could be like, "this is for a family emergency and without leave I'll have to resign")
Obviously that's just one example, different employers' policies will vary. People in my team used standard LWOP for things like, taking a baby to visit relatives overseas, honeymoons, supporting family members through challenges, etc, but my employer was pretty family-friendly so I don't know how well other employers would treat such requests.