I've been working in consulting for 8 years. As far as I can see cost and costs are practically interchangeable in English - I can't offer any rule for clarification.
about your sentence: I would write - "Such economic relevance is a strong indicator for investigating / studying / examining the factors influencing the cost of software over its entire life cycle."

Ich habe mir mal die LEO-Einträge unter "Kosten" angesehen. Da geht cost/costs für mich regellos wild durcheinander.
Den letzten Eintrag finde ich aufschlussreich: total cost of ownership = gesamte Kosten...über die Lebensdauer.
Damit müsste es m.E. in Deinem Fall "(total)cost(ohne s) of software" heißen.