First off, don't feel like a failure. Just because you're "not cutting" it now doesn't mean you'll never get there. It also doesn't mean you wouldn't cut it at another hospital system.
Is there a way you can change preceptor and extend to 4 weeks? Layout a plan to tighten things up? Good educators and management wouldn't just toss you aside after 12 weeks. For my orientation at a level 1 trauma ICU became almost 5 months because I struggled but I made it. My preceptor laid out what I was doing wrong.
The ultimate choice is yours but I encourage you to seek out more options than what they gave you. A third option could be to try for 4 more weeks and if you're not where they want you to be talk to your previous unit manager and see if you could transfer back. Look into policies as well about termination. Express that as an option that you love the hospital system. However, I will say that the grass can be greener and it also isn't always greener. It's a double edged sword but sometimes leaving one system and learning at another would be helpful.
Good luck! Take it from someone who has experienced multiple failures. I failed my EMT course the first time. I was told I wouldn't work in a level 1 trauma ICU. I was told that I wouldn't cut it to become a flight nurse. I'm annoyingly persistent and did all those things. Be annoyingly persistent because stranger I believe in you.