I don't know if they only need to change the wait_timeout. A good hosting company should be familiar with the error "MySQL has gone away" and know what it means and know the different variables that come into play to fix it.

and if it is not good company? jajaja. the stranger is that recently who happens constantly, before he did not happen. then like it was the subject? That he would have to say to them to hosting?

It could be happening more recently because you either have more users on your site (bots count as users too) or because something else changed on the server.

What did your hosting company say when you told them about the errors?

they say to me that they do not know so that of the error and say that he is mine so that this in my data base

You can always asked for server optimization here - Server Configuration
But, you need to read this thread first - [Required]: Info for optimisation / troubleshooting requests [31/03/08 update]

they suspended the page to me by these errors, they always ask to me that them of the Link of when happens and they do not understand that always happens, that I do?

it is possible that this causes consumption of resources of the system of my server?

yes & no, mysql has gone away, its NOT answering anymore, your users will still request the pages and apache will continue to answer even tho mysql isn't, so yes it will cause resources to be used even tho the site is not functioning anymore.

you need to modify my.cnf and make some adjustments to the mysql settings, but without looking at the server itself, we can not really tell you what settings need to be changed to help compensate for the mysql issue.

you can either post for a paid request to have the server checked by a capable person here or post at vb.com and wait for George/Eva to answer your post.