Forgot Colleague's Birthday Twice - Oops!

So uh, I totally forgot my colleague Alex's birthday again this year. It was yesterday actually, and it's the second time in a row I've missed it. Yeah, I have an excuse because my calendar is literally packed to the brim with coding sessions and meetings for new projects at work, but still... how can I just ignore something so personal? Alex has been such a great friend these past couple of years, helping me out with tricky debugging issues when I'm stuck late into the night. And now they're probably wondering if I even care anymore. I tried to send them an email this morning, apologizing and hoping it wasn't too awkward to bring up again after last year's flub, but Alex hasn't replied yet. Maybe they're busy too? Or maybe... oh no, did I just blow any chance of a real friendship here? Now that I think about it, there was a time when we could joke around and talk more casually outside the office context. But now it feels like all our conversations are just work-related... Anyway, sorry for rambling on so much - I guess what I'm wondering is, how do you handle situations where your personal relationships start feeling overshadowed by your professional ones? Anyone else ever in this position? Comments welcome!