Is the issue specifically with the second file, or having both open at the same time? If it is having both open at the same time, create a folder in your local folders, and drag the files into Thunderbird. Once they are in the folder you created, you can probably open them at the same time just like other e-mails within Thunderbird. If you specifically want to be able to open two .eml files at the same time without doing that and can't no matter which two .eml files, then you may want to file a bug report (I assume this is possible, but I don't know how/where).

It's with the second and next. I try first to open one and it works fine, but when I try to open others it doesn't work.

It sounds like the files that aren't working are likely corrupt or perhaps not properly designated as .eml files. When you say "Thunderbird doesn't do it" do you mean Thunderbird doesn't launch, or do you mean it tries to open the file and returns an error? The error could be helpful in the latter case, as could information about where the file came from. In the former case, FYI, when I drag attached .eml files (from e-mails forwarded as attachments) to my desktop, they are named "Inbox" (as opposed to Inbox.eml). I rename them to add the .eml and then I can open them with Thunderbird, but otherwise I will be prompted by Windows for what to do with them.