continually
Happening again and again over time, with short breaks.
Continually means happening repeatedly or frequently over time, with breaks in between. When something happens continually, it keeps occurring again and again, but not necessarily without stopping.
If your little brother continually interrupts you while you're reading, he doesn't interrupt you every single second without pause. He interrupts, you start reading again, then he interrupts again later. The interruptions keep happening, but there are gaps between them. A leaky faucet that drips continually makes one drop, then another, then another, with tiny pauses between each drip.
This differs from continuously, which means happening without any break at all. A river flows continuously because the water never stops moving. But a train that runs continually between two cities makes the same trip over and over, stopping completely between trips.
People often use continually when describing annoying or persistent problems: a phone that continually loses its charge, a shoe that continually comes untied, or a student who continually forgets their homework. The repetition is what matters. When something keeps coming back or happening again despite your wishes otherwise, that's something happening continually.