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
I usually bought when there's a clear pattern already form during the dip then wait for the confirmation. I rarely experience the one you mention on my current trading portfolio since I always set a SL on all my positions when I'm entering position during dip. It's important to watch critical level if there's a downtrend after you enter a position since there's always a possibility for a rejection.
But yeah I understand what you feel because I do experience that most of the time during my newbie trader days.

In a normal circumstances, an average trader knows quit well that cryptocurrency investment is something you will go directly to purchase when it's in the dip market. I understand that cryptocurrency have a particular face and duration foe investors to in, in order to invest and also make sustainable profit per investment. I will say that it's the reason why people do adventure in the investment immediately the market is at dip.
the market is down = buy, the market is up = sell, yes that's the trading formula,
moreover we are in the crypto market, where the market is very volatile, just look today,
a lot of altcoins are down -5% more to -10% because of the bitcoin price down,
this is why we are required not to be greedy when trading