It's very, very easy for higher prestige Big 6 schools to take recruits from your team if you're D prestige. Prestige is HUGELY important in D1, unlike D2 and D3. For every full letter grade a team has you out-prestiged, you need to put in roughly 40% more effort than they do to win the recruit. So if distances were the same and the Big 10 school had C prestige and spent $20,000 on the kid, you'd need to spend roughly $28,000+ to win the battle. And given you aren't in a full conference with $20k+ in post-season cash, beating Big 6 schools is very, very tough. Also, if you are on the lower end of D prestige (so, close to D-) and the other school had a high C prestige, you'd need to outspend them by closer to 50%.
The Big East school probably saw you were in a battle with a Big 10 school, realized you were weak, and came in and snatched a recruit you couldn't protect. This is the norm in D1. If you battle a school right out of the gates in D1 and have a lower prestige, other teams are going to know you're weak and will look to poach (I don't believe in this term, but it's what gets thrown around all the time, so I'll use it) at signings.
At D prestige your goal should not be to bring in the best recruits that will talk to you....your goal should be to sign lower-rated guys with lots of high/high potential that can develop into good players in 2-3 seasons. Big 6 schools tend to not go after these types of players. I don't know which recruits you lost or which Big 6 schools came in on you, but my gut tells me you probably aimed too high at D prestige.