Is this a pop or imap mail account?

Server settings say IMAP

In order for us to better investigate this issue you need to add a little more non-personal information.

Please add the troubleshooting information to your post To find the Troubleshooting information:

• Open Help (or click on three-line-icon and select Help)
• Choose Troubleshooting Information
• Use the button Copy to clipboard to select all. Do not check box "Include account names"!
• Paste this in your post.

Please also add the result of these troubleshooting steps to your post

• Does Thunderbird work in TB Safe mode (see Thunderbird Safe Mode)?
• Do you use anti-virus and firewall software? What is the version?

Application Basics

   Name: Thunderbird
   Version: 45.3.0
   User Agent: Mozilla/5.0 (Windows NT 10.0; WOW64; rv:45.0) Gecko/20100101 Thunderbird/45.3.0
   Profile Folder: Show Folder

             (Local drive)
   Application Build ID: 20160825102941
   Enabled Plugins: about:plugins
   Build Configuration: about:buildconfig
   Memory Use: about:memory

 Mail and News Accounts
   account1:
     INCOMING: account1, , (imap) imap-mail.outlook.com:993, SSL, passwordCleartext
     OUTGOING: , smtp-mail.outlook.com:587, alwaysSTARTTLS, passwordCleartext, true

   account2:
     INCOMING: account2, , (none) Local Folders, plain, passwordCleartext

   account3:
     INCOMING: account3, , (imap) imap.gmail.com:993, SSL, OAuth2
     OUTGOING: , smtp.gmail.com:465, SSL, OAuth2, true

 Crash Reports

 Extensions
   Lightning, 4.7.3, true, {e2fda1a4-762b-4020-b5ad-a41df1933103}

 Important Modified Preferences

   Name: Value

     accessibility.lastLoadDate: 1473557849
     browser.cache.disk.capacity: 358400
     browser.cache.disk.filesystem_reported: 1
     browser.cache.disk.smart_size_cached_value: 358400
     browser.cache.disk.smart_size.first_run: false
     browser.cache.disk.smart_size.use_old_max: false
     dom.apps.reset-permissions: true
     extensions.lastAppVersion: 45.3.0
     font.internaluseonly.changed: false
     font.name.monospace.el: Consolas
     font.name.monospace.x-cyrillic: Consolas
     font.name.monospace.x-unicode: Consolas
     font.name.monospace.x-western: Consolas
     font.name.sans-serif.el: Calibri
     font.name.sans-serif.x-cyrillic: Calibri
     font.name.sans-serif.x-unicode: Calibri
     font.name.sans-serif.x-western: Calibri
     font.name.serif.el: Cambria
     font.name.serif.x-cyrillic: Cambria
     font.name.serif.x-unicode: Cambria
     font.name.serif.x-western: Cambria
     font.size.fixed.el: 14
     font.size.fixed.x-cyrillic: 14
     font.size.fixed.x-unicode: 14
     font.size.fixed.x-western: 14
     font.size.variable.el: 17
     font.size.variable.x-cyrillic: 17
     font.size.variable.x-unicode: 17
     font.size.variable.x-western: 17
     gfx.crash-guard.glcontext.appVersion: 45.3.0
     gfx.crash-guard.glcontext.deviceID: 0x1916
     gfx.crash-guard.glcontext.driverVersion: 20.19.15.4377
     gfx.crash-guard.glcontext.gfx.driver-init.direct3d11-angle: true
     gfx.crash-guard.glcontext.gfx.driver-init.webgl-angle: true
     gfx.crash-guard.glcontext.gfx.driver-init.webgl-angle-force-d3d11: false
     gfx.crash-guard.glcontext.gfx.driver-init.webgl-angle-force-warp: false
     gfx.crash-guard.glcontext.gfx.driver-init.webgl-angle-try-d3d11: true
     gfx.crash-guard.status.glcontext: 2
     mail.openMessageBehavior.version: 1
     mail.winsearch.firstRunDone: true
     mailnews.database.global.datastore.id: 5c7dc23e-c5b2-4d42-9db9-757e2db2e00
     network.cookie.prefsMigrated: true
     network.predictor.cleaned-up: true
     places.database.lastMaintenance: 1473260064
     places.history.expiration.transient_current_max_pages: 104858
     plugin.importedState: true

 Graphics

     Adapter Description: Intel(R) HD Graphics 520
     Vendor ID: 0x8086
     Device ID: 0x1916
     Adapter RAM: Unknown
     Adapter Drivers: igdumdim64 igd10iumd64 igd10iumd64 igd12umd64 igdumdim32 igd10iumd32 igd10iumd32 igd12umd32
     Driver Version: 20.19.15.4377
     Driver Date: 1-25-2016
     Direct2D Enabled: false
     DirectWrite Enabled: false (10.0.14393.0)
     ClearType Parameters: ClearType parameters not found
     WebGL Renderer: Google Inc. -- ANGLE (Intel(R) HD Graphics 520 Direct3D11 vs_5_0 ps_5_0) -- OpenGL ES 2.0 (ANGLE 2.1.0.316930d51ea9)
     GPU Accelerated Windows: 0

     AzureCanvasBackend: skia
     AzureSkiaAccelerated: 0
     AzureFallbackCanvasBackend: cairo
     AzureContentBackend: cairo

 JavaScript

 Incremental GC: 1

 Accessibility

   Activated: 1
   Prevent Accessibility: 0

 Library Versions

     Expected minimum version
     Version in use

     NSPR
     4.12
     4.12

     NSS
     3.21.1 Basic ECC
     3.21.1 Basic ECC

     NSS Util
     3.21.1
     3.21.1

     NSS SSL
     3.21.1 Basic ECC
     3.21.1 Basic ECC

     NSS S/MIME
     3.21.1 Basic ECC
     3.21.1 Basic ECC

I use "Webroot Secure Anywhere" anti-virus & firewall, however this problem occurred prior to using it, when I had Avast anti-virus

Do you access your mail using another device? perhaps one using POP and deleting the mail from the server?

What you describe sounds a lot like an IMAP server synchronizing deletes that happened on another device between Thunderbird starts. IF it is your outlook.com account try looking in the deleted > pop folder and see if your mail is there, as that is the default location they place mail deleted by other applications.

I access this e-mail via either my desktop or laptop computers ( both windows 10) or my "smart" phone. No idea what it uses.

I suggest you brush up on the mail protocol used on all three. But I would start with the phone, they appear to like using pop for some reason.