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 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 http://files.ots.treas.gov/481121.pdf; it is technically a guide for lenders with regard to account management, but does cover your reductions and terminations of lines of credit and the conditions under which these events can occur.
A 25-year expert observer of the mortgage and consumer debt markets, Keith Gumbinger has been cited in thousands of articles covering a wide range of consumer finance and economic topics in outlets ranging from the Wall Street Journal to the Bottom Line newsletters. He has been a featured guest on national broadcasts for CNN, CNBC, ABC, CBS and NBC television networks and has been heard on NPR and other national and local radio programs. Keith is the primary researcher and writer for HSH.com's MarketTrends newsletter and has authored or co-authored a number of consumer guides on mortgages, home equity, refinancing and more.