Rather than simply re-caulking, I suggest removing the vent completely, cleaning everything carefully and re-mount with an appropriate sealant. In my experience, once a roof-mounted vent, skylight, etc. has leaked, the sealant under the flange has failed, at least in spots.
I agree with Thom that sealing with Eternabond tape is the way to go, once it's properly mounted.
Depending on the overall condition of your vent, you might want to consider replacing it. You can replace it with a current model similar to what you have or upgrade.
Winnebago publishes "Sealant Call-Out Sheets" and here's the link to the one for your MH: http://www.winnebagoind.com/diagram/..._d_sealant.pdf
And some more info on Winnebago Sealants: https://winnebagoind.com/resources/s...t%20Sheets.pdf
Winnebago part #131264-03-01A cross-references to Nuco 311: https://www.amazon.com/NUCO-Self-Lev.../dp/B00NUKWY5G
According to the info in the second PDF, #131264-05-02A is non-self-leveling, which I surmise is used under the flange.