Frustrated callers tweeted HM Revenue and Customs (HMRC) more than 11,500 times over the past year to complain about long waits to be answered.
Citizens Advice said those who complained via Twitter claimed to have spent an average of 47 minutes waiting to speak to someone at HMRC, noting that official figures suggested an average wait of 10 minutes.
The charity said one caller tweeted that they had tried to get through to HMRC on four occasions, waiting an hour each time.
Citizens Advice looked at complaints made to the @HMRCgovuk Twitter account between September last year and August after those seeking help from the charity reported not being able to get through to HMRC to resolve issues.
The charity said it helped with 295,000 queries in the past 12 months which could have required people to contact HMRC.
Three out of four of the cases specifically related to tax credits, while others included income tax, National Insurance contributions and child benefit.
An additional 67,000 people visit the tax credit pages of the Citizens Advice website every month, making it the third most visited section, the charity said.
It warned that the roll-out of Universal Credit and changes to tax credits could mean waiting times would further increase.
In June HMRC said it was setting £45 million aside to improve customer service after figures showed that 7.2 million phone calls - or more than one in 10 (11%) - made to it in the past year went through to a "busy" tone instead of the caller being able to speak to someone.
Some months were particularly stretched, with as many as one in five (20.8%) customers hearing a busy tone and being unable to join a phone queue in September 2014.
Citizens Advice chief executive Gillian Guy said: "People are paying the price for not getting through to HMRC. From fines for not completing a tax return in time to under or overpayments for tax credits, people can be left out of pocket because they cannot speak to HMRC on the phone.
"Work and caring responsibilities means not everyone will be able to wait for three quarters of an hour to ask HMRC a question.
"We have consistently raised this issue with the Government. But evidence from across the Citizens Advice service, and our new research, shows HMRC is still failing to provide a timely service.
"There is already a clear demand to be able to speak to HMRC. With the roll-out of Universal Credit and big changes to tax credits just around the corner this is only going to grow. HMRC needs to urgently address the problems many people are experiencing with phone lines."