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I've heard anecdotes about high-interest savings accounts (4.5% around 2006, even 8% in the 80s), that were opened when interest rates (federal funds rate) were high. The implication seemed to be that for some of these accounts, if one were to hold these accounts open, they'd still be getting the same rates after all these years. Do I misunderstand, or is this actually possible?

Flexible savings accounts are almost all variable interest, meaning the rates go up and down with market rates. The reason for this is that if they did not, people could pay into the fixed interest ones when rates elsewhere were low, and take money out when rates elsewhere were high (and invest it at a higher rate in other accounts), making a profit at the bank's expense.

There is a vehicle for 'locking in' savings at high interest rates. This is an account where the interest rate is fixed, but the money is also locked into it. In America these are called Certificate of Deposit (CD). In Canada they are called Guaranteed Investment Certificates (GIC). In the UK and other places they are called Term Deposits. In essence you agree to lock your money into an account for a fixed amount of time, in return for a guaranteed rate of return. (There is usually a clause that allows you to take your money out early, often with a penalty.)

I've heard anecdotes about high-interest savings accounts (4.5% around 2006, even 8% in the 80s).

Well, you heard wrong (g). In 1980-81 the Fed Funds rate peaked at 17.36%. Taxable money market funds were paying over 17%. Short term CDs were over 18%. The 10 and 30 year treasury bonds were over 15%. Baa corporate bonds were paying over 16%. Long term treasury and corporate bonds locked in these rates.

I was fairly new to the market then. A market mentor of mine had recently retired and had sold his business for $600k. He put the bulk of it in 20-30 paper and happily cut coupons at an average rate of 15% until maturity. Think about that. 15% on say $500k is a tidy income of $75k per year. Not bad at all.