Entering shows is tricky and after reviewing the entries to our shows I would make a few suggestions that may improve your chances of being a winner.
The biggest problem I saw was that the series entries can be a problem simply because you are judged on the entire suite of illustrations. All three to five images have to be excellent; many times three out of the five were great but the one or two that were weaker eliminated your entry from being in the show. What I do in shows is enter the series but also enter the top three pieces as single entries as well--five if I can afford it. That way I have a better chance of getting something in the show, and it has happened that both the series and the singles get into the show because once judges like a piece they will always rank it high. So instead of getting nothing in the show you could have multiple pieces accepted.
The other thing is to know what judges are looking for, unfortunately not all shows are judged equally. Looking at shows you can see a pattern of what the organization is looking for and they will usually select judges to give them that type off outcome. You'll find traditional and non-traditional shows, select your work accordingly. If you see that there are a lot of comics being accepted in previous shows then enter, if not, don't. But don't be afraid of entering strong pieces in any category in any show, good work will always be recognized.
Also be concerned with the categories. A few things to keep in mind: Generally speaking, children's books should be entered in children's book competitions; entering them in the Books category makes it much tougher to be recognized. The more obtuse category is Unpublished and what I find is that there is a lot of work in this category that would do better in the Self-Promotion category. What judges look for in Unpublished is what should or could have been published but wasn't. Don't confuse it as self-promotion though if it is a strong image it can be entered in both categories. Also enter your more experimental work as this is a perfect place to show a new way of image making. Judges are looking for new ways of making images which is a good way to get work in a show.
Gallery is another one where it seems that illustrators are selecting work that probably is better in the Unpublished category. What judges look for here is different than commissioned works, they're looking for work that may or may not relate to the artist's general style but stands out as a work of fine art. If you have prints of your commissioned work that you're selling they would do better in the Self-Promotion category rather than in the Gallery.
What I also find is that concept is king in all categories, judges are looking for fresh ideas and ones that are easily recognized. As a suggestion: If you feel you have a complex entry that could use some explanation it would be better to submit the entry in context, while it will only appear as the illustration in the annual, judges will have a good opportunity to see it in its application.
And it's important not to be discouraged, a lot of the entries almost made it into the show--I think our percentage of really good work is better than a lot of shows so keep entering. I saw a lot of really good pieces that had a shot of being in the show.