1. Lack of Industry Knowledge
It's not enough to just know the nuts and bolts of resume writing. You must also know how to manage clients, how to manage your time, and pricing strategies. Start by writing resumes for friends and family, and then for pay for the individuals they refer to you. Join a professional association and study what others do, and then adapt their methods and make them your own.
2. Lack of Vision
What do you want from your resume writing business? Extra income, a bridge to self-employment, or a full-time income? How are you going to get from here to there? If you want to launch a full-scale business, but don't want to invest in marketing and promoting your services, you will be sadly disappointed. I don't care if you create a full business plan, but at least think through your marketing tactics, income-and-expense projections, and pricing strategy.
3. Poor Market Strategy
Speaking of pricing strategy, what is yours? What kinds of clients will you serve? Will you be a general practitioner, or a specialist? Focus on one geographic area, or serve clients everywhere with your web presence? How will you find clients? How will you cultivate referral sources? Will the clients pay what you need to charge them?
4. Failure to Establish Goals
Where do you see your business in six months? A year? Five years? I had a five-year plan and it worked for 10 years ... but now I'm thinking I need to start all over again, and see what I need to do to prepare for the next year ... and five years from now. Set goals not just for income, but number of clients, referral sources you can cultivate, and plans for continuing education and certification.
5. Inadequate Capitalization
This is probably the thing that does most businesses in. You over-estimate your revenue, and underestimate your expenses. A crisis comes along (car breakdown, health issue) and you can't afford to be self-employed. Create a financial safety net with your savings, or by working a part-time job. Diversify your income by writing, or teaching, or subcontracting.