I keep getting kicked out of Safari when online. Is there a way to reinstall Safari?

Reset the device:

Press and hold the Sleep/Wake button and the Home button together for at least ten seconds, until the Apple logo appears.

If that doesn't help, tap Settings > General > Reset > Reset All Settings

If that doesn't help, tap Settings > General > Reset > Reset Network Settings

You will have to re enter your Wi-Fi password.

No data is lost due to a reset.

This is the iPad forum, so I will assume you are referring to iPad's Safari in iOS.

No, you cannot reinstall only Safari. You can restore your iPad by plugging it in to iTunes, letting it sync, and then choose "Restore" from iTunes' menu. That will reload Safari and the rest of iOS.