Just jumping in here from a perspective of someone who puts on a (small)concert series and has done some performing as well. Luck, talent, skill, dedication, etc. all play a part. Personal connections, be it family members in the business or influential friends, can help too in facilitating a performer getting gigs they wouldn't have gotten otherwise. Let's say you're trudging along, playing small folk clubs, and someone you know gets you a spot in a prestigious venue or festival. You then list this venue as a place you've played, and it tends to 'raise your stature'. And lets say you know someone who writes reviews for a well known publication, and your CD gets a good review. (The good review may be well deserved, but as we all know reviewers are swamped with CDs from unknown performers, and the personal connection might be necessary in order to get the CD listened to in the first place). Thats another feather in your cap that raises your profile.

In a sense, you either have 'connections' or you don't, but connections can be nurtured (and I'm not talking about fawning and brown nosing)- but just being friendly and courteous.

Professionalism and dedication is definitely a quality that is totally under the artist's control, and I think it can make or break a performer. That includes such things as showing up on time for the sound check, having a well rehearsed, well prepared set of songs or tunes that is appropriate for the venue, and having good publicity material, including hi res photos. I've been amazed at the talented people that either don't have websites or whose websites are very poorly done or outdated, provide no bio or quotes for me to use when I advertise their concerts, don't follow up, don't answer emails or return phone calls.   Publicity does make a difference, and for a performer, being good at self promotion (without taking it over the top into arrogance) is an important asset.