I have been in business about 2 years now, but mostly towards patisserie (desserts, dry cakes, pastries etc) and simple cakes and have always had very good reviews. I have recently forayed into cake designing and decorating. So far I have had good feedback.
A few days ago one of my returning clients ordered a cake for her little boy's 4th birthday. The cake was to be in the shape of a number 4.
I accepted the order, worked out the details with her. No advance was paid, since she was a regular of mine. I started working on the cake and once the crumb coat was made, I knew the design looked off proportion. I worked on it for a few hours and made it look decent but I could tell it looked home made and no where near as professional as my usual products.
I sent her a picture, she wasn't happy. I offered to make another cake asap, but with barely 4 hours left for the party I wasn't able to make another in time, though I tried (baked fresh cakes). Informed her the same and apologized profusely. She was nice enough and said nothing nasty. She called me an hour later and asked for the first cake as she wasn't able to arrange for one in the short notice. I personally dropped the cake off. I refused any money, though she said she would get back in touch after the party. I should have showed the cake to her while I was there but I dropped off the boxed cake and left. So I have no idea about her reaction on seeing it personally.
Its been 2 days now and I haven't heard from her. This is my first big failure and I feel awful for pretty much ruining a little kid's birthday. It wasn't intentional but it was definitely a complete failure on my part. I am not expecting any money from here but I am wondering if I should text her to ask about the taste or just let it slide and cross a client off my list. I know it tastes great but it was such a dent in my confidence that I cant bring myself to text/call her.

No, you don't have to call her. You didn't take money from her. And please don't think that you ruined  four year olds birthday, and don't cross her name out from your customers list. 

quirky, the kid doesn't know anything except that it's his party and he has friends, cake and gifts. You didn't ruin his birthday at all. I bet he loved the cake.  I wouldn't call her but don't take her off your list she might be willing to give it another shot since you made it right by not charging her for it.

Thank you for the very prompt replies. Helped calm my nerves a lot. Will take your advice surely! Thank you so much.

Quirky, we are often our own worst critics. Sometimes when I finish a cake I see every tiny flaw, but I know from experience that the majority of customers (at least the ones I deal with) never see any imperfections. I've finished cakes before that I was less than thrilled with but that got rave reviews from customers. I'm sure your cake was a big hit and the little boy was delighted. Don't be too hard on yourself. :)

Jselle, I think the fact that the client saw a picture of the cake and did not want it says that it was not really acceptable.  She only took it because she could not get hold of another one at such short notice and the fact that she has not rung back would imply that she is still not happy about the whole situation. I would let it rest, Quirky, and hope that she does return as a customer in the future.

I know I am playing Devil's Advocate but you do not BUY a custom cake for a child's 4th birthday so much for the child as for yourself.  It is not about what the child thought, it is about what the mother thought.  And as far as Quirky's business goes it is about what the other mothers at the party thought.  It is all fine and well to sugar coat when it is personal but when it is a business it is a different matter.  I am not saying you should dwell on it, Quirky, it is done.  What I am trying to say is think about your business.  Do not take on jobs that you do not have the experience for or you will eventually get a reputation as being unreliable and that will flow across to the pastry side of your business as well.  Practice carving and techniques so that when you do get an order you know what you are doing.