How long do you have to be "successful" when you accept investment money?

I have been considering getting an angel investor or joining an incubator. How long do you have to be "successful"? What is successful to an investor?

More details I'm working on a project that may take a year or two to be successful. If I accept enough money to run one year and then I don't get another investor and run out of money without enough to operate is the business considered failed? What if I took a job and continued to work on it in my free time and a year later it becomes profitable? Can the investors close a business down or prevent it from being successful after a certain period (since they own part of the company). I hope you get what I'm trying to ask with this question.

UPDATE Answering questions below:

1. How did you reach to the conclusion it'll take 1-2 years to be "successful"?

   I'm just estimating on the amount of work and then doubling it after hearing stories from a few other businesses that said it took longer than they thought. Also, there are many challenges that I haven't solved yet.

2. What is successful?

   Successful to me would be making enough money to run the company and earn a profit. Making it sustainable. Being able to pay back investors. Let me add that I don't know how a typical investor(s) would want to be paid back. Well, what I've read is that investors are paid back if I sell the company or if I go public and they can then sell the stocks on the stock market. Maybe, I'll add this as another question.

You're asking several questions here:

1. When is a business is considered to be a failure.
2. What is successful for investor.
3. When should I accept outside money and/or mentor ship.
4. How do investors look at moonlighting (working on a venture on your own free time)
5. Can investors shut me down?

I'll try to answer to the best of my experience

1. A business is "never" a failure, it's only a failure when you stop working on it, ideas evolve, and what you learnt in 2-3 months of work, although it didn't bring you to the goals you set out to achieve, it did give you insights on how to get there, if your experience wasn't insightful, than you probably have blind spots and you should check yourself to see that you aren't too emotionally involved in a certain aspect of the business or a certain way of doing things. Most of the ideas can be validated as business models (after a long and arduous way), just because you didn't figure out how to monetize something, doesn't mean that someone else won't, which is exactly why ideas aren't as important as execution power (which is a whole set of tools).
2. Success for investors is really simple: get a big, fat ROI, in a certain sense, they don't give a f&$k about your idea or how much you think you can change the world.
3. Mentor ship - always seek mentor ship from people who already struggled with the issues you're facing, it can be technological, managerial, judicial or otherwise, few are the people who solved the big problem you're facing, but many are those who solved the small problems. Outside money - Don't accept outside money until you have to, the longer you can go on your own money while validating your business model, the stronger your business case will be, and the less %'s of your company will you have to sell.
4. Accelerators & Investors will demand that you'll be working on your venture full time, it show alot of belief in your idea the fact that you're betting your own money on it, and not working on anything else means just that. Ofcourse - take it with a grain of salt, having money to feed you & your family is more important(IMO) :). Incubators will care less.
5. Most investors will let you retain control of your company, but it really depends on the contract that you signed with them.

And the questions I want to ask are:
1. How did you reach to the conclusion it'll take 1-2 years to be "successful"?
2. What is even successful in your own book?