There is no reason your brain clone won't be able to change after it is trained, just like you continue to change based on your experiences. One of the parameters that you will specify for your brain clone is its neuroplasticity - how rapidly it modifies itself based on its experiences. If you set the neuroplasticity to a low value, your clone will resemble you for much longer, but it will also be more likely to appear antiquated. However, if you set the neuroplasticity to a high value, your clone will adopt modern views, but could abandon your core beliefs.
The neuroplasticity setting will not affect learning outside of your personality. The processing of current events and scientific discoveries shouldn't be restrained. But neuroplasticity will be key to how long your brain clone appears to think like you.