Quick question.
Have you ever bought the dip, but then the price breaks through the support and continues dropping deeper for weeks or months?

Well, I have done it before.
The problem may not be panicking but may be determining the actual dip before a pump.
Not every dip is worth buying
That is the biggest risk of buying the dip and truth to be told there is no way to mitigate it completely, after all no one can predict what the market is going to do with complete accuracy so buying the dip still has some risks associated with it, still I think it is a good strategy, however it is one that requires a constant influx of capital to your fiat accounts so in the case the dip keeps getting larger you still have some capital available to buy the next dip.
If that is the case, then don't buy all in. The market will eventually create more opportunities to buy once the market dumps more so you have to manage your funds so you can still avail in the next dip to come. Although this is the best time to buy, but if you know you are lacking funds right now, then just stay calm and patient, and never resort into panic selling because that will mean selling at a loss. Just hold your coins, for sure the market will not always be dumping.