I think you have to weigh the type of travel it is, meaning does 50% mean that you are gone for two straight weeks a month? Or does it mean 2-3 days a week? Do you have control over it - can you plan meetings for days that you know you won't have kid events?
I am a single parent, and my kids are now 8 & 10. I've been traveling about 35% on average for most of their lives and do have full custody (marriage failed for non travel/work related issues about 4 years ago). However, there are very very few trips (like 2 a year) where I am gone more than 3 days at a time, and most (probably 80%) of my trips are either day trips or one night. Some months I'm home for 3 weeks at a time, but that is the nature of my job - it is project based and sometimes my projects align where no travel is needed for 3 weeks.
I DO have the flexibility to say I can't travel on the day of the school musical, or their birthdays, the day I promised to take them to the waterpark or whatever. It doesn't mean I'm not doing my job fully (to reply to whomever said that) - it means my job respects that I have a life and they don't own me. Even more, I take them along with me whenever I'm traveling somewhere that I have someone who can watch them while I'm working - for example a city where we have a friend or relative who doesn't mind hanging out with them for 3 hours while I go to a meeting. Later this month we are going to Asia for a vacation which ends in a meeting for me there. They've had a great opportunity to see the world that they would never have had otherwise.
When I'm not on the road, I work from home. When I add it up, I'm home and actually with them much more at 35% travel than I was working in an office. Yes, I do miss them, but as a single parent with 100% custody, a day or two where I get to be a human and not just mommy is actually nice. And no different than any other divorced situation where the father would have visitation. My job pays very well, and I'm grateful every day that I can provide for my kids (no child support) without having to worry about making ends meet. Lots of single parents aren't as lucky. I don't feel like I've missed too much. For me (and for my children, who are happy, healthy, secure and do have me at all of their important events) this works. I know that isn't true for everyone, but for us, it does - and if any of the variables I described above changed, it probably would not work for me.
So, despite the resounding no chorus above me, take into account all the aspects: what can you control, what will it mean, and will the negative outweigh the positive... before you decide.