I had a problem similar to yours with Skype 4.5. Reverting to this more reliable older Skype 126.96.36.19982 version, resolved the problem for many of us with smart-phones. Others, usually with tablets, reported that Skype 188.8.131.5273, better suited their needs. If you have a smart-phone, tap the link of the former Skype, or the latter if you have a tablet. If your first choice does not meet your needs, the other would be worth trying.
Before tapping the downloaded apk file to install the selected Skype, uninstall the current Skype, disable the Play Store “Auto-update apps” option, and enable the Android Settings (from) “Unknown sources” option. Once installed, disable the “Unknown sources” option. Be sure to try any future Skype release, indicated by a change of release date on the Google Play Store Skype “UPDATE” page. If the new Skype is unsatisfactory, revert to the older Skype using the saved apk file.
You can choose an even earlier Skype version if you feel that this would be beneficial. To date. I have not experienced any security problems with any of the above web links. Please be sure to post another reply to let me know how you go with the installation. I should be able to help you if you encounter difficulties.
If you have not already done so, you should create a good Android issue report here to help Skype improve future versions. I am sure that a Private Message to Claudius, letting him know where your report is, would be a nice surprise, and really make his day