Any hardware does get weaker over time, even CPU get weaker over time as semiconductor chips suffer a a series of changes called as ageing that increases the delay of circuit route. Such changes happen inside CPU due to analogue circuits mainly used for clock generation, thermal sensor, power supply, etc.
To fix this issue, modern architecture dealing with ageing effect by adopting resilient architectures.
The increased delays can cause faults that are corrected by repeating the operation. This re-computation effort is understood as a “slow down” by the user. This methodology however has its limits and eventually the faults cannot be recovered thus resulting in computational errors.
With the reduction of the performance, the clock circuit may fail to lock (short of settle/stable) at certain high frequency and the circuit may have to down clock or throttle.
Thermal sensor inside the CPU may also experience the same issue and may give less accurate value.
The power supply network in the CPU also experiences the same issue and may degrade to certain level where functionally certain circuit block (clock for example) are not able to achieve certain speed.
I have not seen any actual unit in my life that has been observed having this specific issue, but technically it may happen when noticed for more than 5-10 years. So a CPU that can reach 4.6 GHz boost frequency may only able to reach 4.5 GHz boost frequency after 10 years.
On the other hand, high speed communication such PCIe, USB and DDR are very likely to have this long term performance degradation issue. The unit that drive that GHz signal to the board will get weaker and more errors will happen and it will slow down the whole system.
For example in DDR memory, system with ECC such in server or high end laptop motherboard will detect the error and the CPU will do retry to get the right bits from the memory modules.
This will ultimately slow down the performance of the CPU. So YES, a CPU does get weaker over time. But we tend to upgrade desktop and laptop in less than 5 years, so it is not noticeable in real life.