Actually, haven’t faced this issue before. Maybe you have some page time-out while you assign your simple products to configurable.
To make sure that this issue is with your admin, but not with database itself, I offer you to assign your simples to configurable products via desktop application called Store Manager for Magento. It works directly with database and is not web-based, so do not require much server resources.
Also using this application you will be able in bulk to assign simple products to appropriate configurable for that you need in column _associated_sku in front of each configurable product indicate SKUs of simple products separated by comma. Check this article for the details - http://www.mag-manager.com/useful-articles/tipstricks/what-is-magento-configurable-product-and-how-to-import-magento-configurable-products
The free 2-weeks trial version of Store Manager you can download here -
If the issue remains, then most likely it is some deeper issue than admin difficulty and you have to dig for some other reason of it.