According to the CP (Portuguese Railway), http://www.cp.pt, there are two trains daily running from Elvas through Portalegre to Entroncamento with onwards connections to Lisbon Gare Oriente where you can connect to trains to Faro.
Trains leave Portalegre:
Dept Portalegre: 06.19 Arr. Lisbon Gare Oriente 10:02
Dept: Lisbon Gare Oriente 10:20 Arr. Faro 14:20
Dept Portalegre: 15.24 Arr. Lisbon Gare Oriente 19:02
Dept: Lisbon Gare Oriente 19:20 Arr. Faro 23:20 (Only operates Fridays year round and 1st June throughh 31st August.)
The line through Portalegre runs in an east - west direction and only has a link to Faro via Lisbon. The station is situated 12km from the town in a southerly direction. The Council website indicates that there are local buses serving the station.
See this link (in Portuguese) from the council website here:
http://www.cm-portalegre.pt/page.php?page=622
Note that the daily Lisbon - Madrid Express train that used to pass through nearby Castelo de Vide no longer operates that route. It currently runs via Vilar Formoso near Guarda
