Steps to Reproduce:
Let use a project object as the process primary object
1. Go to Administration > Studio > Objects
2. Create an attribute based on static list lookup. 
Example: My project area attribute tied to "Project Area" lookup (id. PBK_LKP_PRJ_AREA)
3. Go to Administration > Data Administration > Processes 
4. Create a new process.
   Primary object: Project
   Start option: Update
   Start Condition: ( Project My project area = 'Project Charter' ) 
   Link the Start step to the Finih Step
   Validate and Activate it
5. Find below screenshot on what the auto-start condition looks like

<Please see attached file for image>

6. Go to Administration > Data Administration > Lookups
7. Filter by "Project Area" lookup (id. PBK_LKP_PRJ_AREA)
8. Go to the Values and deactivate the Project Charter value
9. Go back to the process we created and go to the "Start options" tab

<Please see attached file for image>

Expected results: The auto-start condition to display as it was set
Actual results: The auto-start condition has vanished and is blank.

Any CA PPM release

This is the expected behavior: The Auto-Start condition that was initially set is not valid any longer
Please reactivate the inactivated lookup or recreate a new valid auto-start condition

As the auto-start condition is not visible any longer, you might want to check at DB level what the condition was. This will help you analyze what the condition was and what criteria is currently not valid.

Query to find all auto-start conditions on the system
 
select bdp.id, cc.name, bdp.process_code, ofe.expression from bpm_def_processes bdp, cmn_captions_nls cc,
bpm_def_process_versions bdpv, odf_filter_expressions ofe
where cc.table_name = 'BPM_DEF_PROCESSES'
AND bdp.id = cc.pk_id
AND cc.language_code = 'en'
AND bdpv.process_id = bdp.id
AND ofe.object_code = 'BPM_DEF_PROCESS_VERSIONS'
AND ofe.object_instance_id = bdpv.id

The same theory applies to sub-page display conditions. Please check the below KB:
kb000076792