Penalty or sandbox?

This year, I have several new websites (1~2 months old) which used to get good SERP for 1 or 2 weeks , and then dropped suddenly.
I found them easy to get good rank with the help of constant blog posts and articles writing. But always the SERP can't last long.

And usually before a SERP drop, near all of them had a apparent rank rise ( main search terms get into page 1).
According to webmaster tools link report, they all have hundreds or around a thousand of backlinks, and no more than 100 domains.

I thought that might be some kind of penalty and stopped link building for these websites. Sometimes I also remove some backlinks and send Google reconsideration, which seems to be helpless.

I am always wondering if there is another possibility that Google uses this method to test new websites authority.
Google finds a new website get a lot of fresh backlinks and then put it into sandbox. If the website can still get constant and good authority backlinks, the SERP will recover or get even better.

Should I give up these websites or just ignore the SERP change and continue to build good backlinks or social signals?

If you have stopped building backlinks start building again and see if the sites will recover their ranking.

Before building new back links I suggest you to remove the crappy links at first. It will take a lot of time and labor to deindex the links. But you should at first do this.