No. The IRS states that you are required to keep copies of your own form 8606's for your entire life. (This is an exception to the usual rule that tax forms can be discarded after 3 or 7 years.) Your online transcript should go back 10 years, but you may want to log in and download your information now, before the 10th year gets erased and replaced with this year.
https://www.irs.gov/individuals/get-transcript
Your most recent form 8606 should have a running total of the after-tax basis in your traditional IRA, and should be the only form 8606 you need to file your current return. However, if audited, the IRS does not have to allow any adjustment that you can prove, and even though you might have sent them the forms in the past, they don't have to (and probably can't) produce them for you, you have to prove it to them. So you should get and keep copies of all your prior form 8606s.
