Relegated Hampshire were reinstated ahead of Division Two runners-up Kent.
Kennedy is due to meet Colin Graves, the chairman of the England & Wales Cricket Board, to discuss the matter.
"If you lose confidence in the people you are dealing with, it is quite difficult to continue," Kennedy said.
"I feel completely let down by the ECB and I will put forward Kent's case [at the meeting] to see if anything can be done to reverse the situation or give us some comfort that we're not being singled out for all the wrong reasons.
"A lot depends on the answers we get over the next few days, but if I am completely and utterly shouted down I will have to think about if it is worthwhile continuing."
The issue arose after Durham were relegated on Monday, having accepted a £3.8m financial aid package from the ECB.
Kennedy also expressed displeasure in the manner in which he discovered the ECB's decision not to promote Kent, claiming he found out after being contacted by a journalist.
"The ECB decided to telephone Hampshire and tell them they were staying up and I found out by having a call from a journalist at a national newspaper who asked me what I thought," Kennedy told BBC Radio Kent.
"One team were told they were staying up and they ignored the team that lost the battle but I haven't given up by any means. I won't let Kent down, I will fight this for as long as it takes."
Kent chairman George Kennedy has said he is considering his position over the club's failure to be promoted following Durham's relegation from Division One because of financial issues.