I am not from Laminar Research; just a flight simmer from downunder.
It is always advisable to attach your log.txt file to your question, not the XPlane installer log.txt file as it can sometimes provide a simple solution. The required file is generated immediately after a formal shutdown or a crash.
What version of X-Plane are you running? Is it the original and official version from Laminar Research or the steam version which is a 3rd party hybrid (modified) version not supported by Laminar.
If you search through the X-Plane website and trawl through the "knowledge base" information area you will find that one of the requirements of running or using the digital download version of X-Plane is you need to be connected to the internet at all times when using the software.
When you are "flying" the software performs a "silent or secret" background check to determine that you are running a legal copy ie somebody else does not have the same product code, by checking you product code agrees with their records or you are not running two copies at the same time.
Unfortunately there is also a company that sells dodgy or pirate versions of X-Plane and supplies a pirated product key. The software will only run for 24 hours and the user is locked out.
The software will give you a "grace period" and if you have not been connected for some time you will be asked to provide the product key as you are experiencing at present. Alternatively it may push you back to a demo version. The worst case situation is a total lockout.
There are 389 pages of questions with answers in this forum and I have read every Q&A since page 8 when I joined the forum.
When this forum did have a moderator full time from Laminar Research, to oversee this forum, the answer I have seen from LR staff in responding to your problem is to make sure you are connected to the internet at all times.
In reviewing your question and re-reading the first sentence, there is no serial key provided with any update. The original product key supplied with your original purchase is applicable for all XP11 updates. I would suggest you apply the product code and ensure you are connected to the internet at all times when flying.
If you are unsatisfied with my answer then contact Laminar Research direct at firstname.lastname@example.org