Hi @Chris Franklin,
My company has done similar things in the past. However, they were for specific sales or events, (ie Black Friday) and were sent much closer together.
A few things we did that might help - we made sure to change the subject line and pre-header; I feel if they are exactly the same it might look more like spam (but have not hard evidence of this). Also, if someone opened or clicked on the first email, they were excluded from the second email; if a they clicked or opened the second OR first email, they were excluded from the third email and so on (again, our emails were sent much closer together).
Hopefully someone who has more experience or knowledge can chime in here as well; I honestly don’t know about the potential fallout from re-sending a campaign.