There's a page about this service on the Argentinian government website. All the information is in an image (accessibility? what's that?). The image is dated 21/05/2019.
The service operates from Monday to Friday. (There is no mention of public holidays, but you should double-check if you travel on a day that's a holiday in either country.) Trains depart every 30 min all day: from Posadas from 07:15 to 18:15, from Encarnación from 07:30 to 18:30. The trip takes 8 minutes. The fare since 02/02/2019 is AR$56 or ₲12000.
The page mentions that you need to have your passport (presumably with applicable visa) or identity card (presumably for Paraguayans and Argentinians only). There is additional information for minors (you may need to show that you have the proper vaccinations and that your parents authorized the trip). If you pass the border with products purchased in the other country, you need to go through customs (sector de Aduanas).
If the service is suspended or modified, hopefully there would be a mention on the service modifications page.
Please note that I have no local knowledge and am just reporting what I found on the web.