The Mac Studio randomly turns off the display of one screen.

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'different cables' is a check against cables that are broken. What many users are discovering is that their assumptions about 'which cables are good enough' do not work at high resolutions and refresh rates.

For HDMI cables, there is a huge change in technology at higher than 4K at 60 Hz. Above that, certified cables labeled "ULTRA" or "48K" are required.

for USB cables, length should be 1 meter or shorter.

for Thunderbolt cables, lengths should generally be 0.5 meters or shorter. There is an Apple super-engineered 0.8 meter cable that also works. Thunderbolt-5 cables provide NO data rates advantage and do not get around the length limits.

what exact make&model displays are using, and what cables, adapters and docks are in the data stream?

the Eizo FlexScan L568 Appears to be a 1920 by 1200 display with DisplayPort, DVI, and analog VGA (D-sub) inputs.

adapter/cables from USB should have the USB section of the cable strictly limited to one meter or less.

for DisplayPort, the DisplayPort section of the cable should also be limited to one meter or less.

for DVI or HDMI, that portion of the cable does not have strong length limitations as long as resolutions are 4K at 30 Hz or less.

the Eizo FlexScan S1921 appears to be a 1280 by 1024 display with DVI and analog VGA inputs.

for DVI or HDMI, that portion of the cable does not have strong length limitations as long as resolutions are 4K at 30 Hz or less.

Your Mac Studio M1 from 2021 or later features HDMI 2.0, whose Direct HDMI port can run up to 4K at 60 Hz for HDMI or DVI, provided high quality certified "Premium" or "Ultra" cables are used at highest resolutions.

these cables are not strongly length-limited when used with HDMI 2.0.

The Eizo FlexScan L568 appears to be a 1280 by 1024 display with DVI and Analog VGA inputs.

for DVI or HDMI, that portion of the cable does not have strong length limitations as long as resolutions are 4K at 30 Hz or less.

if you are meeting all those length limits, consider the possibility that the adapter may have failed.

The video capabilities for your Mac are excellent.

The problem is in the many converters and adapters and cables required, and Apple's failure to spell out EXACTLY how long these cables should be, but insisting that cables that make errors will cause the display to drop out.

4K at 60 Hz is the upper limit for HDMI 2.0. (beyond that HDMI changes completely.)

So sorry, 4K at 30 Hz was not intended to be a recommendation, that was my error. I intended to change that to read 4K at 60 Hz but the change got lost.

This cable: "USB-C to DisplayPort cable from the brand KabelDirekt (2 m – USB-C to DisplayPort adapter cable" is too long for reliable operation, and should be replaced with a shorter cable or a different solution.

For DVI, you can buy a simple "just wires" converter or converter cable HDMI <-> DVI as long as you stay below the limit for direct conversion from HDMI, which is 1920 wide (or HD, or 4K at 60 Hz).

There is no Master List that I know about. The market is chaotic because manufacturers do not deeply understand what they are selling, and it is mostly modern Macs that are saying NO to data attenuation errors on long cables.

The length of the cables must be shorter to meet the standards for TOP SPEED transmission on these cables, and that means one meter or shorter for the USB-C and/or DisplayPort portions of the cable.

as long as the display is no wider than 1920 wide, the HDMI --> DVI adapter is a "just wires" adapter. There is no length limit on HDMI cables at modest resolutions.

perhaps the cable or adapter (or display) has failed. Can you substitute other know-good items to find out?

a USB-DVI or similar adapter must keep the USB section of the cabling under one meter. Once it converts to HDMI or DVI, the length of that portion of the cabling can be up to several meters, up to 4K at 30 Hz resolution.

Mac Studio M1 MAX should easily support five displays at far higher resolutions than you are using. We have not seen reports here of problems supporting many displays, only reports of cables that were not high enough spec to accomplish their task without dropping out.

There is one more really old problem we used to run into, that might still be vexing you today:

The power levels required for regular HDMI or DVI (which are higher than DisplayPort) are in limited supply in LOTS of computer systems. Years ago, we used to say that if you wanted to run more than TWO non-DisplayPort displays, you needed to be using at least one ACTIVE HDMI or DVI adapter. (or switch at least one away from HDMI or DVI) these more expensive adapters contain re-driver circuitry, so that the computer did not run out of the higher Voltage power needed for HDMI or DVI.

Users who did either suddenly found their third display perked up and worked without issue.

if you are already running at least one of your three displays using DisplayPort, then this 'at most two Legacy = non-DisplayPort displays' limitation should not apply to you.

I try to talk about a few of the side issue that might apply as we go along, because this discussion will be here for a long time, and others may find it by searching.