We are able to afford multiple vacations a year. I believe, most of it would apply for people going to Disney multiple times.
1. High income. Graduate degree in a hot field does it. If not available, you will have to both work and live frugally.
2. Low cost of living area. While you get paid more in NYC and SF Bay area, it's only 10-30% more, and your costs are at least 50% more.
3. Not buying a big house. Many families at our income level live in $500K houses. We decided to spend half as much for a condo.
4. Not carrying any debt outside of mortgage. Yes, you have to save for a car, but you are less likely to splurge for a car when the money is coming out of your pocket.
5. Have a vacation savings account

6. Staying in cramped accommodations while on site or staying off site. I am absolutely floored by the number of people willing to spend a week, 4 people in one tiny room. That's my personal idea of vacation hell

, but it does save you some major $.
7. Driving to WDW. We are ~15 hours away, and I personally would not consider driving. Yet, many people do it twice a year to save money.
8. Going at low season times. The accommodations and flights are going to be cheaper.
9. Not doing much in terms of table service or character meals. That one I totally understand - if you are going to WDW twice a year, you can do one character meal at time, and it's going to be enough.
So for a family of 4 (2 kids), 7 days at slow time at a value resort will be $800 with tax, plus $1,300 for dining, plus $1,300 for park tickets, plus $200 for gas, plus $300 for incidentals, $3,900 total. For that, you need to deposit $300 every two weeks into your vacation account.