There's no fixed waiting period after a TN refusal, but timing depends on how long it takes to gather evidence that actually addresses the stated reason. Rushing a near-identical resubmission is usually slower in the end than taking time to fix the real gap.
Let the fix set the timeline, not the calendar
Some gaps close quickly; a clearer duty letter can be drafted in days. Others take longer, like a credential evaluation or a change in employer structure. Set milestones around the actual evidence needed rather than an arbitrary date, and confirm with counsel when the file is genuinely ready rather than simply ready to submit again.
There is also a reason not to move quickly that has nothing to do with preparation. A second request made days after a refusal, on materially the same facts, invites the question of what changed, and the honest answer at that point is usually nothing. Allow enough time for the change to be real and documented, then present it plainly.
Where the employer needs cover in the interim, that is a staffing question to be solved separately rather than a reason to compress the immigration one, and saying so early usually produces a better conversation than discovering it after a second attempt.