Are you using the most recent 1.0.7 version?
Do you see anything suspicious in /Applications/Utilites/Console.app when you try to launch the app by any chance? To see messages related to Manuscripts, you can filter for messages that note the word "Manuscripts".
If you could copy the contents of the log and send to us via email@example.com (which remains private to the development team of two), that would help us a lot.
I have a few a few possible ideas for workarounds:
Does rebooting the computer help? This is rather unlikely to have an effect but I would like to rule out something strange on the bootup time you are currently on inducing it.
Does clearing the settings and cache directory created by Manuscripts application help? To clear Manuscripts into its "factory settings", please complete the following steps:
Go > Go To Folder (or hit Shift+Command+G)
Enter ~/Library/Containers into the window that opened and then click "Go"
Once you've done that your Finder window should be now in a folder where you see the folder "com.manuscripts.Manuscripts".
Please drag the folder com.manuscripts.Manuscripts into Trash (this clears the cache directory that contains safely deletable information that improves the performance of Manuscripts and which it uses when exporting documents, etc).
Copy and paste the following into the terminal window, and hit Enter after:
defaults delete com.manuscripts.Manuscripts
CEO & Co-founder of Manuscripts.app Ltd