Computers are failing to run inventories because they do not have the Inventory Plug-in. They show that they have the Inventory Rule Agent but this is not the actual Inventory Plug-in.
First check that the Inventory Plug Install Policy is properly configured. Go to Settings>Agent/Plug-ins>Discovery and Inventory>Windows/UNIX/Linux/Mac>Inventory Plug-in Install. Make sure that the policy is turned on and change the schedule option from Once ASAP to By schedule. Click Add schedule>Schedule time (or Window), specify a time, then click No repeat and change it to Day. Making the schedule repeat will make the Inventory Plug-in try to install again in case something didn't work on the first try.
Make sure the computers that need the Inventory Plug-in are targeted by the Inventory Plug-in Install Policy. In the Inventory Plug-in Install Policy select the default target (All Computers without Inventory Plug-in), click the pencil (Edit) button above, in the new window that opens click Update results and verify that the computers that need the Inventory Plug-in are listed. If not their agents may not be functioning or the database may not be receiving their basic inventories.
If the computers have been targeted by the Inventory Plug-in policy but have still not installed the Inventory Plug-in after several scheduled attempts then their agents may be corrupted. The corrupted agents can be uninstalled through the Actions>Agents/Plug-ins>Push Symantec Management Agent page or through the command prompt by running AeXAgentUtil.exe /uninstallplugins and then AeXAgentUtil.exe /clean. AeXAgentUtil.exe can be located in C:\Program Files\Altiris\Altiris Agent or wherever the Agent installation directory is.
If the computers still do not install the Inventory Plug-in after their agents have been reinstalled and the Inventory Plug-in Install Policy has ran again then there may be leftover inventory files from a previous corrupted installation. Go to C:\Program Files (x86)\Altiris\Altiris Agent\Agents\Inventory Agent and delete the Inventory Agent folder if it has files in it.