'MySQL 4' is not very precise. 4.0x and 4.1x are very different – but probably not very important here.
There have been quite a lot of problems with Wine on Ubuntu 11.x – both 11.04 and 11.10. For 11.04 we have this FAQ: http://www.webyog.co…ould-i-do.html. Did you replace the .dll's or are you able to run SQLyog on Ubuntu 11.04 on your environment without doing so?
Please also tell the exact SQLyog version you are using. We may not be able to do anything about this but we should at least try if there was a recent change causing this.
I don't think SQLyog crashes as such. But a(ll) GUI program(s) will of´ course disappear if the complete graphics system does. Also after this 'crash' does the 'wineserver' process still run? In Wine SQLyog does no have its own process but is 'encapsulated' in the 'wineserver' process. (and BTW: I do not like that you refer SQLyog as 'a badly behaving program')