If you used paid advertising, such as Adwords, etc. and then stopped. Did your site's visitors/income decrease to the level previous to using Adwords? Did it increase dramatically?
I don't think it will affect your visitors especially if you continue with other advertising program and implement different method to increase traffic.
If you only use Adwords and then stop using them then your traffic will slow down and slowly tickle of after a few years depending on the quality of your site. If you have a very interesting site then your traffic could either stay similar or even increase if it is viral.
yes i experienced this. when i stopped using Adwords, my site's visitor decreased. sometime we have to choose keywords with less competitors or less searches (but more potential for visitor to buy) then, try to put capture page or squeeze page. it is to capture the users name and email address (and sometimes more depending on your industry). your visitors will give you their first name and email address so that you could start to build a relationship with them. One more thing, do your site look like professional designs or not. it plays important role for visitors to buy or join.
If your site is something unique and interesting the word of mouth will work verry well, and you can get more visitors.
When your SITE is new you'd notice that. After a while, when you have uniques, you won't lose users dramatically.