Great question – appreciate you asking.
Short answer: yes, the Regenerate Character die must make a second roll because of Deadly.
Reference the Turn Order sequence:
Attack Step
1. Declare Attackers
2. Declare Blockers
3. Use Action Dice and Global abilities
4. Assign Combat Damage
5. Apply “when damaged” abilities
6. Resolve Damage and “when KO’d” abilities
Then the Clean-Up Step.
Per Rule 2.7.6.2:
If a Character die has the Regenerate keyword ability and that die is KO’d, apply the Regenerate ability immediately (effectively interrupting the resolution of damage).
This means that if the Character die with Regenerate is KO’d by combat damage or a KO ability other than Deadly, it would make the Regenerate roll in sub-step 6 of the Attack Step.
Per point (2) under the Deadly keyword (in Appendix 1):
Deadly is a Persistent ability. Therefore, it is resolved in the Clean Up Step.
Germane to the situation cited, the Regenerate Character die would make a second roll in the Clean-Up step to avoid the Deadly effect. This is also covered in point (3) under the Regenerate keyword (in Appendix 1):
A Character die with Regenerate would still be rerolled when KO’d by a Deadly keyword ability.
Thematically, think of the action as being stabbed with a poisoned blade. You apply a dressing to keep from bleeding to death (i.e. avoiding the potential KO from combat damage), but you’ll need a second treatment to survive the blade’s poison (i.e. avoiding the Deadly effect).