I can see how this might happen, but it's also a very good way to establish credibility with other customers (and funders, if you're looking to go that route). IME, it all but eliminates questions about "are you too small?" if you're already doing business with a big, well-known company.
You should try to ascertain whether they are likely to be aligned with your other customers in terms of feature development, and seek to find other large-ish customers so that you're not totally dependent upon that one. You should also try to make the dependence bilateral — make it so that you're delivering tons of unique value to them, so that they can't say "add X feature or we're dropping you".
I looked around and found one or two articles that essentially said "If one customer is more than x percentage of your revenue, time to diversify. Start actively drumming up new business."
If you are so small that you can't actively look to take on more customers because they take up all your time and you don't want to gamble on hiring more help when you don't really need it, you have a problem.
This seems to be partly a self created issue. Small businesses seem to think "We're friends!"
No, you aren't and big businesses know that having dealt with enough assholes themselves already.
No one can make you work only for them but the reality is if you want to stay a one-man operation and not hire more people and this one customer is 80 percent of your revenue, the tendency is to feel like "This works!" -- until it suddenly doesn't and they have you over a barrel.
Yeah, if you've got 80% of your revenue coming from one customer, that's not great. But it all depends on how you work with your customers. In my business, things are pretty hands-off, and we have calls only a couple times a year, largely to talk about promoting our work together (our tech is a customer-facing differentiator for them, so we give joint talks at conferences and such).
I don't think there's some magic percentage, over which you need to diversify. You should always be looking to get other customers, and if you have one big one then it should be easier to get other big/medium-sized ones.
You should try to ascertain whether they are likely to be aligned with your other customers in terms of feature development, and seek to find other large-ish customers so that you're not totally dependent upon that one. You should also try to make the dependence bilateral — make it so that you're delivering tons of unique value to them, so that they can't say "add X feature or we're dropping you".