Although softwares are different many will detect entries from previously installed versions either in the registry or other hidden files which are not removed during a normal uninstall routine, so no you may not get a new trial time even if you didn't use the previous version for the full trial period,sometimes you can find those hidden entries and remove them though it is not normally easy.
Trials are not there to provide you with softwre that has a life span of "30 days" but to encourage you to by a product if you like it, the product does not generally change fundamentally in nature between versions so if you liked one version the next would be presumbly suitable, not withstanding <oldversion.com>
A far better approach would be to look for alternative freeware softwares that dont have those problems and may even do a better job with less resources.
I think there is a free uncrippled version of roboform in the forum though I havn't checked if it installs over later versions.