iPod Touch 5th Generation Unchangable incorrect Time/Date

I have a 5th Generation iPod touch. I've owned it for about three years now, but for the past 3 months it has been broken just enough to be frustrating, but not enough to warrant replacement (Nothing warrants replacement though, it is a 64GB and I spend a lot of hard earned money to get it).

My problems started with the time resetting every time I locked the device. No warning, no drops, no dunks. It suddenly out of the blue started happening. I've done multiple resets, I've checked the calendar setting and made sure they are Gregorian. I updated to 8.4 and sill had the problems. I've tried recovery mode, and watched it as it sets up find and set itself to the wrong time. Annoyed as I was, I could set the time and date back to their proper settings and the clock would run while the iPod was unlocked and in use, and sometimes while charging. Ironically enough, Siri could give me the correct day (or time), but not the right time (or day).

I've since tried ios 9 beta, still had issues, I restored from beta, and still had issues. My WiFi would constantly cut out while I was browsing for no explanation, I thought it was tied to the time problem.

However, today the problem escalated past mere annoyance; I left it uncharged for a few days, and now my time and date is set to December 31, 1969. I tried to manually set the date back to today, and the date picker ALWAYS jumps past 2015; I've fought with it for about half an hour now and every time I get close, the year jumps to 2020 and then the directions of the years reverse (scrolling down, through the month, makes the year jump back). It has gotten so that I click the date picker wheel TWICE DOWN and it jumps from 2010 to 1998. I've tried resetting it twice, and both times the date is no closer to correct. My computer time is accurate, and I connect it to WiFi, but nothing works now.

Am I just doomed beyond saving it now?