In a situation like this, as long as you're not begging for work and feeling needy, you won't come across as needy. Flaky people are those who say they are going to do something and then they don't do it. Hence the term "he flaked."
The concern your contacts will have is that if they hire you, you will be unable to fulfill your duties because you may be called away suddenly for a family emergency. Therefore, you have to decide with whom you have a strong enough relationship to share what's happening in your life, in the hope that they will be understanding and hire you for short term and day playing jobs to keep you working.
For the rest, you can re-establish by sharing the good things that have been going on, complimenting them on something they've worked on, and seeking advice on basic things like networking events to join and charity organizations to get involved in. This way the maintenance of your relationship can be set around your involvement, as opposed to trying to get work from them.
When your family issues reach a resolve that you feel comfortable committing to longer jobs, you'll be in touch with enough people to reach out to.
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