Digital signature becomes invalid when one of the colleague signs it.

In short: The originally signed PDF contains errors which start to cause validation issues as soon as more data (your signature) is added to the file.

In detail:

Validation of a signature in Acrobat consists of two major parts:

• The embedded signature container is checked, in particular whether it is correctly embedded, whether the contained hash values match the corresponding data, and whether the signer identity is valid.
• If there are additional data after the PDF revision covered by the signature, then the changes induced by these data are checked. Depending on some settings of the signature only certain kinds of changes are allowed here.

While the first part usually is content with checking the file as it is, the second part (if there are additional data) apparently enforces that actually a repaired version of the PDF is checked, not the file as is, if there are errors in the document... anywhere in the document! And repairs do invalidate signatures.

So if you have a document with errors and sign it once (without prior repair), the signature usually looks ok. But as soon as you append any extras, e.g. a second signature, the initial signature becomes invalid.

In your case there are a number of errors in the original document "Idejni projekt - DM 38.pdf". In particular there are a number of form fields (signature form fields to be precise) associated with some document pages but those fields cannot be reached from the fields in the global AcroForm Fields collection.

You can see this if you browse through all the pages. Initially your signature panel looks like this

but after leafing through the pages (giving Acrobat a chance to find all those disconnected form fields) it looks like this:

and after validating all signatures like this

Here the signature by Dario Janic is the one covering the whole document. Thus, while validating it, Acrobat validates the file as is, so in spite of the obvious issues the result still can (and here is) validated ok.

After you added your signature, though, the result is:

Now Dario Janic's signature is not covering the whole PDF anymore, part two of the validation kicks in, sees all the errors, and causes the validation to work on a repaired PDF. Your signature, on the other hand, covers the whole document and, therefore, your signature is validated ok. If you applied yet another signature, your signature also would start to be invalid.

The cause of this most likely is that to create the original document a number of files were merged without properly handling existing form fields: When merging documents, one has to either collect all the fields (renaming them if needed) in the AcroForm Fields of the merged PDF or flatten them (i.e. adding their appearance to the static page content and dropping the fields and their widget annotations altogether). In particular filled signature fields should be flattened as merging will invalidate them anyways.

In the PDF metadata stream PDFsharp is mentioned as creator tool, so I assume the faulty merge has been executed using that PDF library. 

In the Dario Janic signature metadata Acrobat Reader is mentioned as signing application. So apparently the merging result created by PDFsharp has been signed with Acrobat Reader; without looking at all the pages , though, otherwise Acrobat likely would have seen the errors and required a repair before signing.

To fix this please ask the previous signer to use a file that is merged properly.