I heard a buzz coming from my breaker box. When I pressed on each breaker, one by one, the buzzing stopped when I pressed on one of them.
A few weeks later, the same thing happened, and again when I pressed on that same breaker the buzzing stopped. Is there any danger here? Does that breaker need to be replaced?
If the buzzing stops when you press on the breaker, and the load is constant, it likely means a loose connection to the panel buss. Loose buss and wire connections cause heat and arcing which have the potential to start a fire. Sometimes the breaker's connection gets loose over time through either improper torqueing or constant heat cycling. More commonly it sees to happen on higher amperage drawing circuits.
Without knowing what kind of panel and what is on the circuit, its harder to make a recommendation. You can certainly replace the breaker if you feel comfortable doing so, however if the breaker's connection to the buss bar is compromised you may not be able to get a good connection and further work may be necessary.