Q: Do banks by law have to give you notice of reductions in a Home Equity Line of Credit?
A: If you mean "advance notification," the answer would be "no," at least in most circumstances. The reduction or termination of a home equity line of credit would not require advance notice if you have signed an agreement permitting the lender to do so when the value of your home has significantly declined below the appraised value, or where a material change in your financial situation has occurred.
That said, the regulation which governs such things suggests that they do need to notify you within 30 days of having taken any "adverse" action on your account.
Somewhere in the paperwork you signed to get your home equity line of credit there is usually a clause which allows the mortgage lender to make a change to your credit line (even terminating it all together) if there is a material change in the property's valuation or even your credit profile. Presumably, you signed or initialed this clause as a part of your agreement.
Some more technical details can be found at here; it is technically a guide for lenders with regard to account management, but does cover reductions and terminations of lines of credit and the conditions under which these events can occur.
