The inner tube on my bikes rear wheel is flat. I pumped it up about 4 days before and rode it a couple days than took a break and when I went to ride it i noticed the air was all gone. I found a small slash on the inside right where this thin piece of plastic keeps the ends of the spokes from poking it, was moved aside so i suspect rubbing against the spoke did it. Should i move that platic thing back over the spokes or buy a better one?

what's the official name for it as well if i need to buy anouther?

Edit: I've also noticed for about a week before the back loses pressure a small bit quicker than the front

Look for a Velox Cotton twill rim strip. It's sticky-backed to stay put.

Heavy duty thorn resistant inner tubes hold air longer because they are thicker.

But they weigh more. a trade off..

It's called rim tape and, yes, you should certainly move it back over the spoke hole inside the rim as it's there to prevent just what happened to your tube. Better yet, but a roll (or two) of Velox rim tape, which is adhesive backed cloth and the world's standard for rim tape. Remove your unreliable thin plastic one and replace it with Velox and, applied properly, it will last as long as the rim. Velox comes in three widths so ask your LBS which one is proper for your rim.

I like Continental Easy Tape rim strip. I have never had it shift out of position and it is thinner than the Velox tape; it takes up less room inside the rim which often makes tire mounting easier.