When there is a sudden drop in earnings the problem is determine whether it is just a one-off occurrence (in which case it is likely to be a good buying opportunity) or is it a sign of things to come (in which case it is probably not a time to buy).
Fortunately for sensible investors, basically, the market prices stocks as if any drop in earnings is going to be permanent. If it turns out to be a one-off, a purchase is likely very good. I recall that Dell had such a dip in 1994 (earnings were even negative). It turned out to be fabulous buying opportunity and since then the price has grown by around 100 times.
Of course, it is never quite so black and white. There might be dip in earnings which, although not permanent at the new level, the growth from now on is lower than historical levels.
Whenever the earnings have been growing smoothly and then they suddenly take a drop, then you have to dig deeper. Is it a simple one-off situation, perhaps due to a large write-off or a temporary market difficulty? Or is it a sign of further problems? In the first case, it may be a good buying an opportunity. In the second, it may be time to move on to another company.
A good place to start looking for a deeper understanding of what is going on is to read carefully the chairman's and CEO's reports in the annual report. Were there any special circumstances? Do they appear to be open with the shareholders? (If they are not, then perhaps they are in denial. Big danger.) Does it make sense what they are saying?
Is the company sticking to its areas of expertise or expanding into areas it knows little about? Whenever possible, talk to people who use the services and products of the company.
If at the end of this you are still unsure, put in an even bigger margin of safety in your estimates. Or, even better, move on to another company.