I've had mine for a year and hasn't... But petsmarts xmas decor paint started to peel as i placed it into the tank! Or you can make your own for cheap with some mesh from a craft store and hot glue. (AKA im not spending $32 on a log! I have 4 from the store and cant believe i spent that much! The other bettas can get mesh logs for only $2.)although i do agree with the floating logs. my betta loves them as well but only problem is the paint on them starts to peel off quickly (at least in my experience)
I find its fine as long as theres plants and not just some ugly spongebob stuff on pink gravel!