Is it normal? Yes, for a relationship that is probably near its end, but not normal for a relationship that you thought was going somewhere.
Sure, we all have moods and times when we're more quiet than others, but if this is happening repeatedly, it's a bad sign. After three months, you guys should really be clicking, not running out of things to talk about. If this had happened on the first date, I doubt you would have had a second one.
Did something change in your relationship? Is one of you going through a hard time? Stress or depression could explain the reticence.
If nothing significant has changed, then your relationship might simply have run its course. Sometimes we have bad dates on the first date, other times it takes 10-15 dates before we run out of common ground. Every relationship has a life span of its own. Obviously you guys hit it off at some point, so maybe you can think about how you did so and rekindle that. It just depends on your situation and how frequent and awkward the silences are.
But, to answer your question, no, frequent awkward silences are not normal for a healthy, thriving relationship.
Love the Sound of Music reference in the tags! It made me smile.
Thanks. I love that movie. Always have. So does Jackie Chan.
Out of things to say after being together only three months? That does sound like a bad sign. If it is like that now, what will you find to talk about after you've been married for three years, or ten, or twenty?
Seems like all the advice I keep getting continually pushes me into the direction of breaking up with him. Thanks for your advice, Cary. I really appreciate it.
Panama, I believe, answered a very similar question recently. I remember saying that this has happened to me twice, and both relationships were over in under two months. That's a more serious red flag as far as I'm concerned.
what about if you are shy/introverted and so is the other person...?
I think if there are special circumstances, you should ask close friends for advice on the relationship. Sometimes friends may be too nice to be brutally honest to our face. I heard this website called Wisemuv (just google search it) helps people get honest anonymous feedback from friends about their relationships. It's really easy to use and looks helpful in deciding what to do about our relationships!