25-year-old Ada joined the Alex from Conference side Histon and was later joined by fellow defender Mat Mitchell-King and Ada has gone on to make 16 appearances in all competitions for the Railwaymen.
Crewe manager Dario Gradi told the Crewe Chronicle "Patrick was pestering me to go. He was virtually on his knees begging.
"So I thought he'd thank me when I said he could go to Rushden for the rest of the season.
"I thought it was done when I got a text from him saying he is going nowhere.
"I think there must be financial implications for him somewhere along the line. I was surprised but he remains a Crewe player."