I believe this is a problem of your server. If the server load is too high or a page requires a lot of mysql queries to display all items this could result in incomplete pages. If this problem happens often, you should ask your webhoster support. Either the server hasn't enough resources for Elgg (shared server?) or isn't configured properly.

It is shared server but I have only 20 users (page is still in development stage) and 64MB of memory for site with 30s execution time.

Unfortunately, the load could be too high even with a single user online. On a shared server it's more likely for this to happen. In my experience a shared server is not powerful enough for Elgg in the long run. If you have many widgets on a page (for example profile page or an index page) there could be up to 100 http requests and even more mysql queries for a page to load. Depending on your server setup it could be a too high CPU load, or maybe the I/O system (hard disc access) is the bottleneck. I also had made the experience that MySQL on a separate server could result in slow page loads / incomplete pages. Back then I was on a shared server (the hoster called it their "cloud server"). It often happened that pages loaded very slowly and were incomplete afterwards. I think the server config was very bad or the routing was the problem. It didn't improve and I had to change to a VPS server (not that everything works fine ALL the time there, but you have at least a few more possibilities to improve the server config and apart from a hardware issue right at the beginning and a temporary routing issue on the webhosters ISP everything works fine since about a year).

Not sure if your issue might be due to the access permission settings on your site. Have you set the default access permission on the Site Administration page to "private"? Although I would have expected only the content of the widgets not being visible with private settings.

If the access permission settings isn't causing the issue: has your problem only started recently or did you have this problem already from the beginning? In the latter case I would say something is wrong with your installation and I would suggest to re-install Elgg (and then also to upgrade to Elgg 1.7.8). If the problem started at a later time I would suspect some 3rd party plugin to be responsible. Then you should disable any non-core plugin to see if the visibility problem stops and then activate one at a time to find out which is causing the problem.

Anyway, upgrading to the latest stable release is always adviseable - if only to get rid of security issues.