What is the frames limit of the mirrorless cameras sensor? When should it be changed (for example on the Sony a6000 series or on the Sony a7)?
Unlike a mirrored camera, there is little likelihood of the sensing system in a mirrorless camera suffering a catastrophic failure so it is really up to your "taste" to determine when a sensor is too old. The primary causes of degradation to a CMOS sensor array are heat, dye neutralization and cosmic rays.
Thermal Degradation Normally thermal damage is so slight that devices become obsolete before it is an issue. If you tend to use your camera frequently in hot conditions or in very hot and very humid conditions, there will be physical degradation to the minute circuitry that makes up the CMOS. This will generally manifest itself as increased dark current noise, standing patterns, or ghosting.
Color Dye Failure Remembering that a color sensor is really just a grayscale sensor with colored dyes over the pixels, we must consider the stability of those dyes. Have you ever seen what happens to be a printed page left on the dash of your car? the sunlight fades whatever ink it touches. The dyes in your camera are not much different. Exposure to light, especially sunlight will cause the dyes to fade. It will take dozens to hundreds of hours of exposure before any measurable degradation occurs and possibly thousands before the degradation is severe enough that it cannot be corrected in post processing. The risk is, however, increased with a mirrorless camera because they are continually staring. While a DSLR is only exposed, on average, for 1/30 sec for every frame, a mirrorless sensor could be exposed for minutes for each frame. If you want to track dye degradation you can image a color target in a known, stable lighting condition and continue to check over time. The last time I checked on a 6-micron sensor I measured 4 delta-E per thousand hours degradation so I would recommend checking every 250 hours of sensor exposure (how many frames that is depends on your implementation.) color dye degradation can appear as a desaturation of the imagery but more frequently takes on a color cast. The color cast is often pink/ yellow as the blue dye breaks down first. Some manufactures will re-calibrate the color transfer curves for little or no cost.
N.B. The bleaching of dyes over time from light exposure is totally unrelated to the damage discussed when asking about photographing the sun directly. That sort of damage is caused by overloading or overheating of specific electronic elements and can occur in a single exposure under the right conditions. Dye bleaching occurs over a long period of time and does not involve the sensor circuitry.
Radiation Damage Cosmic rays really are an issue for silicon electronics. Cameras used on the international space station can become useless after a few months. Studies have shown that even the variations in the height of the earth's surface affect cosmic ray-induced artifact. So if you live in the Andes your sensor's life expectancy is less than if you live next to the dead sea. Cosmic ray (and to a much lesser extent microwave) degradation occurs whether your camera is turned on or not but studies have shown an increase in damage to powered sensors. Radiation damage will manifest as bright or dim pixels. These pixels may appear suddenly and/or may worsen slowly over time. It is also possible to experience column failures and/or increase in shot noise as a result of radiation damage.
Mitigating Degradation Heat damage only occurs while the sensor is running (unless you subject it to absurdly high temperatures.) Avoid situations where the body of the camera becomes warm to the touch and if it is black, consider a white or reflective wrap for photography in summer or direct sunlight. Radiation damage occurs constantly so there is really not much you can do about it aside from not taking your camera on plane trips more the necessary. Dye bleaching occurs any time light strikes the sensor so limiting that will prolong the life of the dyes. Use preview modes as little as possible and if there is no capping mechanism to the sensor (such as a normally closed shutter or optional mirror) make sure the lens cap is in place.
Evaluating Degradation To make sure your mirrorless is working properly and not expired, you should monitor occasionally (every year or 100-250 hours of use) to make sure that none of these issues described exceeds your personal standards. My prediction, though, is that some other part of the camera such as the screen, UI components, or battery/ memory interfaces will fail long before the sensor does.
Footnote I unfortunately cannot link any specifics of my research because it was corporate R&D. I can tell you that we were working with a fleet of around 800 CCD and CMOS sensors which were all shutterless and made 300k to 800k images per year. On average, a CCD sensor lasted about 4 million integrations and 3500 hours of operation before it was retired. The CMOS fared better, averaging about 7 million integrations and 8000 hours operational before they failed.
The sensor on a digital camera is a solid-state device, and while theoretically degradation is possible, in practice, they last basically forever. Don't worry about it.
On the other hand, the mechanical shutter on these cameras does have a finite life, probably normally in the range of 100,000 actuations (although it's not typical for camera makers to give a number for lower-end cameras). But, normally, this isn't something you'd proactively change out — you'd keep using it until the shutter fails, at which point you'd either have it repaired (if you've used a newer or more high-end camera heavily) or just replace the camera.