Today there are no large investors and almost every ico company suffers from a lack of investment. If we analyze the company's ico market, then very few of those who collect at least half of the planned funds.
You would be surprised to see the rate at which large investors will get into the market once the market shows some sign of recovery actually. Looking at the market right now, you will understand that, the chances of recovery are actually getting high by the day. Now, based on the question asked by the OP, most times when the general market looks good, and then we are beginning to see new moneys being pumped into the ICO market, then, we will obviously get to see the chance of tokens rising but no one can tell specifically when or how long this would come into play.
It's complicated. There is no exact answer to it. The price depends on the road map and the stages of its implementation.
But most projects begin to speculate with their tokens within a couple of months after entering the exchange.
Yes, in my observation, many tokens/coin got delisted from exchange after huge dump and low daily volumes. There will be no exact time. It is almost similar to gambling. May get or may not. Only if we are ready to lose some money, that is the right capital to risk with ICOs.