I experienced exactly the same issue on my VPN, which started after installing Utopic HWE kernel 3.16.0 on Ubuntu 14.04 LTS.

Unfortunately most upvoted answers did not solve the problem. After researching I found the root cause of the issue.

Error

Using interface ppp0 Connect: ppp0 <--> /dev/pts/4 sent [LCP ConfReq id=0x1 <asyncmap 0x0> <auth chap MS-v2> <magic 0x792e9abe> <pcomp> <accomp>] sent [LCP ConfReq id=0x1 <asyncmap 0x0> <auth chap MS-v2> <magic 0x792e9abe> <pcomp> <accomp>] sent [LCP ConfReq id=0x1 <asyncmap 0x0> <auth chap MS-v2> <magic 0x792e9abe> <pcomp> <accomp>] sent [LCP ConfReq id=0x1 <asyncmap 0x0> <auth chap MS-v2> <magic 0x792e9abe> <pcomp> <accomp>] sent [LCP ConfReq id=0x1 <asyncmap 0x0> <auth chap MS-v2> <magic 0x792e9abe> <pcomp> <accomp>] sent [LCP ConfReq id=0x1 <asyncmap 0x0> <auth chap MS-v2> <magic 0x792e9abe> <pcomp> <accomp>] sent [LCP ConfReq id=0x1 <asyncmap 0x0> <auth chap MS-v2> <magic 0x792e9abe> <pcomp> <accomp>] sent [LCP ConfReq id=0x1 <asyncmap 0x0> <auth chap MS-v2> <magic 0x792e9abe> <pcomp> <accomp>] sent [LCP ConfReq id=0x1 <asyncmap 0x0> <auth chap MS-v2> <magic 0x792e9abe> <pcomp> <accomp>] sent [LCP ConfReq id=0x1 <asyncmap 0x0> <auth chap MS-v2> <magic 0x792e9abe> <pcomp> <accomp>] LCP: timeout sending Config-Requests Connection terminated. Modem hangup

The root cause was that 2 required netfilter kernel modules are not loaded during boot.

nf_conntrack_pptp nf_conntrack_proto_gre

Solution: load the nf_conntrack_pptp module, the latter is its dependency and will be loaded automatically.

sudo modprobe nf_conntrack_pptp