You seem to imply that reliable ≠ small, and that small registrars are cheaper.
In my experience, the opposite is true in both cases.
Big registrars can’t afford any support costs since they prefer to squeeze the price down as far as possible, and therefore they prefer to simply lose or outright drop any customer in case of any and all problems. Conversely, small registrars may charge more, but have better (i.e. actually existing, and sometimes even dedicated and personal) support for when things go wrong, and have a vested interest in keeping you as a customer.
In my experience, the opposite is true in both cases. Big registrars can’t afford any support costs since they prefer to squeeze the price down as far as possible, and therefore they prefer to simply lose or outright drop any customer in case of any and all problems. Conversely, small registrars may charge more, but have better (i.e. actually existing, and sometimes even dedicated and personal) support for when things go wrong, and have a vested interest in keeping you as a customer.