There are several conditions that apply to these features:

You should normally avoid using hibernate mode while your system is connected. The problem is that the PPPoE protocol requires the Enternet driver to respond to Echo heartbeat packets every minute. Starting with version 1.4, a warning will be posted that EnterNet will disconnect and exit before going into sleep mode.

With Windows 2000, hibernate mode was not supported before version 1.4.

Persistent connection support, from the Advanced Settings menu on EnterNet 300, is not very persistent. Enternet 300 will retry the connection a few times after the server disconnects, and then report the connection was dropped. Persistent connection support is not available in Enternet 300 or EnterNet for Mac OS.

EnterNet uses the SNMP component to update changes to the TCP/IP. There is a known bug in Microsoft's SNMP related to standby mode which could cause delays after reawakening. This is described in the MS Knowledge Base article Q152569. Although the article doesn't mention it, the same behavior has also been seen on Millenium and Windows2000.