I am coming from a Muay Thai style and trying out MMA. When sparring in Muay Thai I would frequently hold my glove to my face and successfully block punches. When doing this in MMA, most punches were passing my much smaller glove. I wonder if this is due to a lack of precision in where I place my hand or whether or not I should not attempt at passively blocking and instead focus on moving my head (bobbing) to avoid punches to my head.
Defending punches by putting a glove against your face is not a successful strategy without big gloves. With MMA's small gloves or without gloves at all, it is a Bad Idea. To be truthful, it's not an optimal strategy in boxing or kickboxing, either: you still take a substantial impact.
Instead, work your rolling, bobbing and weaving, slipping, and parrying, or shell up with your elbows pointed towards the opponent and your hands behind your head.
As you guessed, small gloves aren't ideal for passive blocking (keeping your hands in one position to block more than one punch). The closest thing to passive blocking you could get away with in MMA is to whip your forearm at your opponent's wrist in such a manner that your wrist impacts his. This isn't a strike though, the idea is the get your wrist to stick to his. WIth that in mind, you'll know you're doing it right when you are "catching" his punch with the outside of your wrist and have your arm act as a shock absorber, guiding the punch close to your face, but destroying all its momentum.
That might sound like a long slow movement, but in practice it looks like your swatting away the punch. The secret is to contact and redirect.
That being said, Dave Liepmann's suggestion to turtle up is how everyone else does it, and probably for good reason.