Affects of old design framework on web applications

Does the old or deprecated web design framework has affected on a new web application functions, performance or even compatibility?

it's difficult to tell, you got to do the proper analysis on what technologies currently being used in existing (deprecated) framework and whether these components are still supported in a long run.

you may also consider a business impact analysis to determine the feasibility of integrate your new web app functions into your deprecated web design framework, or you may just start to design a new framework for business sustainability.

To my opinion, yes.

Web development is going so fast, as we don't have the choice to update / maintain code very often.

So if the application have not got any significant update since several years you will need to completely rebuild it.

Usually client side code is the one that fail first because of browser compatibility (Javascript / CSS)
then on server side you will need update .NET  / DB tool to newest version because of end of life support,  security or server update ...

Application are like a car, if you don't do any regular maintenance chances are you won't be able to use it...

Plus chance are that the UI look like an old apps and this is no good for sales (if the apps is on the market) or not fun to use for the end user (if it use only in house).

In our company we have an old design for our Web Application but there are some issues and bugs raises every time for some Web pages controls like Drop down, links,... etc.

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if you do not change the requirement of software, it won't give you trouble.  we have very old framework applications running but we keep the software requirements as per those frameworks...

of course today's world, you need to be upgraded day by day to challenge the performance and security.