We just went through an application with Wells Fargo. (Apparently I have a credit score just over 800. Cool.)
Here's why we withdrew the application. The bank can end the loan if you lose your job or if your house loses significant value. The Venn diagram of when I'd want to use it and when it would be withdrawn is pretty much a circle: need to pay for a few months of expenses until I get a new job, or I discover such a big problem in my house that I can't cash-flow it.
Bonus: when I called, the CSR told me "those disclosures aren't really real, you know." Yeah, that makes me want to do business with you, dude!
Well, that's why you don't deal with Wells Fargo or other for-profit lending institutions--everyone knows that, don't they?. Credit Union for the win!
In all seriousness though, yes, I believe they do reserve the right to freeze it, but I don't think they will (or can?) do that if you lose your job, as how would they even know?? They aren't asking you for pay stubs every month to prove you're still employed. I think their bigger concern (and reason for that disclaimer) is another housing bubble burst that makes it obvious to them that equity has disappeared from everyone's home. They definitely don't want you maxing out your entire HELOC at that time, when they know that that equity doesn't exist anymore. But again, I don't think this is a something they are looking at with individual homes...they aren't rerunning market analyses or ordering appraisals every year on your house to double check the value. A big problem discovered in your home that needs the HELOC funds is not going to be on the bank's radar at all. How would they know your foundation now needs $40k of work done? They don't.
And even if they can pull it from you when you lose your job or house loses value, so what? It's free to have the HELOC once it is opened (well...maybe not at Wells Fargo), so you can still take free advantage of the HELOC benefits up until they decide to yank it away from you if that is what they want to do. And even then, I assume you'd still have another 5 years to pay off any balance you have.