PS1 games playing on PS2 slim often shows black screens

I own a PS2 Slim (SCPH-70004) connected to my tv with the PS2 to HDMI adapter, and I tried to launch Tekken 3. The game boots up normally but can't show the intro cinematic: in fact, the HDMI signal gets lost during the intro but comes back when I skip it or when it ends. While the game plays fine, the problem gets worse with Ridge Racer 4.
The game also have the same intro problem, but the signal gets lost as well when starting a grand prix, and mashing buttons doesn't help.
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PS1 games playing on PS2 slim often shows black screens